Import supplements and repo reorganization

1 files changed, 7774 insertions, 0 deletions

diff --git a/ic_experiments/ml3.c b/ic_experiments/ml3.c
new file mode 100644
index 0000000..7ad3edb
--- /dev/null
+++ b/ic_experiments/ml3.c
@@ -0,0 +1,7774 @@
+/* Generated by Cython 0.22 */
+
+/* BEGIN: Cython Metadata
+{
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+        "depends": []
+    }
+}
+END: Cython Metadata */
+
+#define PY_SSIZE_T_CLEAN
+#ifndef CYTHON_USE_PYLONG_INTERNALS
+#ifdef PYLONG_BITS_IN_DIGIT
+#define CYTHON_USE_PYLONG_INTERNALS 0
+#else
+#include "pyconfig.h"
+#ifdef PYLONG_BITS_IN_DIGIT
+#define CYTHON_USE_PYLONG_INTERNALS 1
+#else
+#define CYTHON_USE_PYLONG_INTERNALS 0
+#endif
+#endif
+#endif
+#include "Python.h"
+#ifndef Py_PYTHON_H
+    #error Python headers needed to compile C extensions, please install development version of Python.
+#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03020000)
+    #error Cython requires Python 2.6+ or Python 3.2+.
+#else
+#define CYTHON_ABI "0_22"
+#include <stddef.h>
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+#define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
+#endif
+#if !defined(WIN32) && !defined(MS_WINDOWS)
+  #ifndef __stdcall
+    #define __stdcall
+  #endif
+  #ifndef __cdecl
+    #define __cdecl
+  #endif
+  #ifndef __fastcall
+    #define __fastcall
+  #endif
+#endif
+#ifndef DL_IMPORT
+  #define DL_IMPORT(t) t
+#endif
+#ifndef DL_EXPORT
+  #define DL_EXPORT(t) t
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+#ifndef PY_LONG_LONG
+  #define PY_LONG_LONG LONG_LONG
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+#ifndef Py_HUGE_VAL
+  #define Py_HUGE_VAL HUGE_VAL
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+#define CYTHON_COMPILING_IN_CPYTHON 0
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+#define CYTHON_COMPILING_IN_PYPY 0
+#define CYTHON_COMPILING_IN_CPYTHON 1
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+  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
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+  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
+  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ? \
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+#endif
+#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
+#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
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+  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
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+#if PY_MAJOR_VERSION >= 3
+  #define PyBaseString_Type            PyUnicode_Type
+  #define PyStringObject               PyUnicodeObject
+  #define PyString_Type                PyUnicode_Type
+  #define PyString_Check               PyUnicode_Check
+  #define PyString_CheckExact          PyUnicode_CheckExact
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
+  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
+#else
+  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
+  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
+#endif
+#ifndef PySet_CheckExact
+  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
+#endif
+#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
+#if PY_MAJOR_VERSION >= 3
+  #define PyIntObject                  PyLongObject
+  #define PyInt_Type                   PyLong_Type
+  #define PyInt_Check(op)              PyLong_Check(op)
+  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
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+  #define PyInt_FromUnicode            PyLong_FromUnicode
+  #define PyInt_FromLong               PyLong_FromLong
+  #define PyInt_FromSize_t             PyLong_FromSize_t
+  #define PyInt_FromSsize_t            PyLong_FromSsize_t
+  #define PyInt_AsLong                 PyLong_AsLong
+  #define PyInt_AS_LONG                PyLong_AS_LONG
+  #define PyInt_AsSsize_t              PyLong_AsSsize_t
+  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
+  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
+  #define PyNumber_Int                 PyNumber_Long
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyBoolObject                 PyLongObject
+#endif
+#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
+  #ifndef PyUnicode_InternFromString
+    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
+  #endif
+#endif
+#if PY_VERSION_HEX < 0x030200A4
+  typedef long Py_hash_t;
+  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
+  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
+#else
+  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
+  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func))
+#else
+  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
+#endif
+#ifndef CYTHON_INLINE
+  #if defined(__GNUC__)
+    #define CYTHON_INLINE __inline__
+  #elif defined(_MSC_VER)
+    #define CYTHON_INLINE __inline
+  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define CYTHON_INLINE inline
+  #else
+    #define CYTHON_INLINE
+  #endif
+#endif
+#ifndef CYTHON_RESTRICT
+  #if defined(__GNUC__)
+    #define CYTHON_RESTRICT __restrict__
+  #elif defined(_MSC_VER) && _MSC_VER >= 1400
+    #define CYTHON_RESTRICT __restrict
+  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define CYTHON_RESTRICT restrict
+  #else
+    #define CYTHON_RESTRICT
+  #endif
+#endif
+#ifdef NAN
+#define __PYX_NAN() ((float) NAN)
+#else
+static CYTHON_INLINE float __PYX_NAN() {
+  /* Initialize NaN. The sign is irrelevant, an exponent with all bits 1 and
+   a nonzero mantissa means NaN. If the first bit in the mantissa is 1, it is
+   a quiet NaN. */
+  float value;
+  memset(&value, 0xFF, sizeof(value));
+  return value;
+}
+#endif
+#define __Pyx_void_to_None(void_result) (void_result, Py_INCREF(Py_None), Py_None)
+#ifdef __cplusplus
+template<typename T>
+void __Pyx_call_destructor(T* x) {
+    x->~T();
+}
+template<typename T>
+class __Pyx_FakeReference {
+  public:
+    __Pyx_FakeReference() : ptr(NULL) { }
+    __Pyx_FakeReference(T& ref) : ptr(&ref) { }
+    T *operator->() { return ptr; }
+    operator T&() { return *ptr; }
+  private:
+    T *ptr;
+};
+#endif
+
+
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
+#else
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
+#endif
+
+#ifndef __PYX_EXTERN_C
+  #ifdef __cplusplus
+    #define __PYX_EXTERN_C extern "C"
+  #else
+    #define __PYX_EXTERN_C extern
+  #endif
+#endif
+
+#if defined(WIN32) || defined(MS_WINDOWS)
+#define _USE_MATH_DEFINES
+#endif
+#include <math.h>
+#define __PYX_HAVE__ml3
+#define __PYX_HAVE_API__ml3
+#include "string.h"
+#include "stdio.h"
+#include "stdlib.h"
+#include "numpy/arrayobject.h"
+#include "numpy/ufuncobject.h"
+#include "math.h"
+#ifdef _OPENMP
+#include <omp.h>
+#endif /* _OPENMP */
+
+#ifdef PYREX_WITHOUT_ASSERTIONS
+#define CYTHON_WITHOUT_ASSERTIONS
+#endif
+
+#ifndef CYTHON_UNUSED
+# if defined(__GNUC__)
+#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
+#     define CYTHON_UNUSED __attribute__ ((__unused__))
+#   else
+#     define CYTHON_UNUSED
+#   endif
+# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
+#   define CYTHON_UNUSED __attribute__ ((__unused__))
+# else
+#   define CYTHON_UNUSED
+# endif
+#endif
+typedef struct {PyObject **p; char *s; const Py_ssize_t n; const char* encoding;
+                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
+
+#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
+#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
+#define __PYX_DEFAULT_STRING_ENCODING ""
+#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
+#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (    \
+    (sizeof(type) < sizeof(Py_ssize_t))  ||             \
+    (sizeof(type) > sizeof(Py_ssize_t) &&               \
+          likely(v < (type)PY_SSIZE_T_MAX ||            \
+                 v == (type)PY_SSIZE_T_MAX)  &&         \
+          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||       \
+                                v == (type)PY_SSIZE_T_MIN)))  ||  \
+    (sizeof(type) == sizeof(Py_ssize_t) &&              \
+          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||        \
+                               v == (type)PY_SSIZE_T_MAX)))  )
+static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject*);
+static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
+#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
+#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
+#define __Pyx_PyBytes_FromString        PyBytes_FromString
+#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
+#if PY_MAJOR_VERSION < 3
+    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#else
+    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
+#endif
+#define __Pyx_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
+#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
+#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
+#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
+#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
+#if PY_MAJOR_VERSION < 3
+static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
+{
+    const Py_UNICODE *u_end = u;
+    while (*u_end++) ;
+    return (size_t)(u_end - u - 1);
+}
+#else
+#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
+#endif
+#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
+#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
+#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
+#define __Pyx_Owned_Py_None(b) (Py_INCREF(Py_None), Py_None)
+#define __Pyx_PyBool_FromLong(b) ((b) ? (Py_INCREF(Py_True), Py_True) : (Py_INCREF(Py_False), Py_False))
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x);
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
+#if CYTHON_COMPILING_IN_CPYTHON
+#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
+#else
+#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
+#endif
+#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+static int __Pyx_sys_getdefaultencoding_not_ascii;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    PyObject* ascii_chars_u = NULL;
+    PyObject* ascii_chars_b = NULL;
+    const char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    if (strcmp(default_encoding_c, "ascii") == 0) {
+        __Pyx_sys_getdefaultencoding_not_ascii = 0;
+    } else {
+        char ascii_chars[128];
+        int c;
+        for (c = 0; c < 128; c++) {
+            ascii_chars[c] = c;
+        }
+        __Pyx_sys_getdefaultencoding_not_ascii = 1;
+        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
+        if (!ascii_chars_u) goto bad;
+        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
+        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
+            PyErr_Format(
+                PyExc_ValueError,
+                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
+                default_encoding_c);
+            goto bad;
+        }
+        Py_DECREF(ascii_chars_u);
+        Py_DECREF(ascii_chars_b);
+    }
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    Py_XDECREF(ascii_chars_u);
+    Py_XDECREF(ascii_chars_b);
+    return -1;
+}
+#endif
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
+#else
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+static char* __PYX_DEFAULT_STRING_ENCODING;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
+    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
+    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    return -1;
+}
+#endif
+#endif
+
+
+/* Test for GCC > 2.95 */
+#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
+  #define likely(x)   __builtin_expect(!!(x), 1)
+  #define unlikely(x) __builtin_expect(!!(x), 0)
+#else /* !__GNUC__ or GCC < 2.95 */
+  #define likely(x)   (x)
+  #define unlikely(x) (x)
+#endif /* __GNUC__ */
+
+static PyObject *__pyx_m;
+static PyObject *__pyx_d;
+static PyObject *__pyx_b;
+static PyObject *__pyx_empty_tuple;
+static PyObject *__pyx_empty_bytes;
+static int __pyx_lineno;
+static int __pyx_clineno = 0;
+static const char * __pyx_cfilenm= __FILE__;
+static const char *__pyx_filename;
+
+#if !defined(CYTHON_CCOMPLEX)
+  #if defined(__cplusplus)
+    #define CYTHON_CCOMPLEX 1
+  #elif defined(_Complex_I)
+    #define CYTHON_CCOMPLEX 1
+  #else
+    #define CYTHON_CCOMPLEX 0
+  #endif
+#endif
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #include <complex>
+  #else
+    #include <complex.h>
+  #endif
+#endif
+#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
+  #undef _Complex_I
+  #define _Complex_I 1.0fj
+#endif
+
+
+static const char *__pyx_f[] = {
+  "ml3.pyx",
+  "__init__.pxd",
+  "type.pxd",
+};
+#define IS_UNSIGNED(type) (((type) -1) > 0)
+struct __Pyx_StructField_;
+#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
+typedef struct {
+  const char* name;
+  struct __Pyx_StructField_* fields;
+  size_t size;
+  size_t arraysize[8];
+  int ndim;
+  char typegroup;
+  char is_unsigned;
+  int flags;
+} __Pyx_TypeInfo;
+typedef struct __Pyx_StructField_ {
+  __Pyx_TypeInfo* type;
+  const char* name;
+  size_t offset;
+} __Pyx_StructField;
+typedef struct {
+  __Pyx_StructField* field;
+  size_t parent_offset;
+} __Pyx_BufFmt_StackElem;
+typedef struct {
+  __Pyx_StructField root;
+  __Pyx_BufFmt_StackElem* head;
+  size_t fmt_offset;
+  size_t new_count, enc_count;
+  size_t struct_alignment;
+  int is_complex;
+  char enc_type;
+  char new_packmode;
+  char enc_packmode;
+  char is_valid_array;
+} __Pyx_BufFmt_Context;
+
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":726
+ * # in Cython to enable them only on the right systems.
+ * 
+ * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ */
+typedef npy_int8 __pyx_t_5numpy_int8_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":727
+ * 
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t
+ */
+typedef npy_int16 __pyx_t_5numpy_int16_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":728
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int64      int64_t
+ * #ctypedef npy_int96      int96_t
+ */
+typedef npy_int32 __pyx_t_5numpy_int32_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":729
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_int96      int96_t
+ * #ctypedef npy_int128     int128_t
+ */
+typedef npy_int64 __pyx_t_5numpy_int64_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":733
+ * #ctypedef npy_int128     int128_t
+ * 
+ * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ */
+typedef npy_uint8 __pyx_t_5numpy_uint8_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":734
+ * 
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t
+ */
+typedef npy_uint16 __pyx_t_5numpy_uint16_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":735
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint64     uint64_t
+ * #ctypedef npy_uint96     uint96_t
+ */
+typedef npy_uint32 __pyx_t_5numpy_uint32_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":736
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_uint96     uint96_t
+ * #ctypedef npy_uint128    uint128_t
+ */
+typedef npy_uint64 __pyx_t_5numpy_uint64_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":740
+ * #ctypedef npy_uint128    uint128_t
+ * 
+ * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_float64    float64_t
+ * #ctypedef npy_float80    float80_t
+ */
+typedef npy_float32 __pyx_t_5numpy_float32_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":741
+ * 
+ * ctypedef npy_float32    float32_t
+ * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_float80    float80_t
+ * #ctypedef npy_float128   float128_t
+ */
+typedef npy_float64 __pyx_t_5numpy_float64_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":750
+ * # The int types are mapped a bit surprising --
+ * # numpy.int corresponds to 'l' and numpy.long to 'q'
+ * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longlong   long_t
+ * ctypedef npy_longlong   longlong_t
+ */
+typedef npy_long __pyx_t_5numpy_int_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":751
+ * # numpy.int corresponds to 'l' and numpy.long to 'q'
+ * ctypedef npy_long       int_t
+ * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longlong   longlong_t
+ * 
+ */
+typedef npy_longlong __pyx_t_5numpy_long_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":752
+ * ctypedef npy_long       int_t
+ * ctypedef npy_longlong   long_t
+ * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_ulong      uint_t
+ */
+typedef npy_longlong __pyx_t_5numpy_longlong_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":754
+ * ctypedef npy_longlong   longlong_t
+ * 
+ * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_ulonglong  ulong_t
+ * ctypedef npy_ulonglong  ulonglong_t
+ */
+typedef npy_ulong __pyx_t_5numpy_uint_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":755
+ * 
+ * ctypedef npy_ulong      uint_t
+ * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ */
+typedef npy_ulonglong __pyx_t_5numpy_ulong_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":756
+ * ctypedef npy_ulong      uint_t
+ * ctypedef npy_ulonglong  ulong_t
+ * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_intp       intp_t
+ */
+typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":758
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uintp      uintp_t
+ * 
+ */
+typedef npy_intp __pyx_t_5numpy_intp_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":759
+ * 
+ * ctypedef npy_intp       intp_t
+ * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_double     float_t
+ */
+typedef npy_uintp __pyx_t_5numpy_uintp_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":761
+ * ctypedef npy_uintp      uintp_t
+ * 
+ * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t
+ */
+typedef npy_double __pyx_t_5numpy_float_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":762
+ * 
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longdouble longdouble_t
+ * 
+ */
+typedef npy_double __pyx_t_5numpy_double_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":763
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_cfloat      cfloat_t
+ */
+typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
+
+/* "ml3.pyx":7
+ * 
+ * DTYPE = np.float64
+ * ctypedef np.float_t DTYPE_t             # <<<<<<<<<<<<<<
+ * 
+ * cdef DTYPE_t weight_success(int dist, int dt, DTYPE_t alpha, DTYPE_t delta,
+ */
+typedef __pyx_t_5numpy_float_t __pyx_t_3ml3_DTYPE_t;
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    typedef ::std::complex< float > __pyx_t_float_complex;
+  #else
+    typedef float _Complex __pyx_t_float_complex;
+  #endif
+#else
+    typedef struct { float real, imag; } __pyx_t_float_complex;
+#endif
+
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    typedef ::std::complex< double > __pyx_t_double_complex;
+  #else
+    typedef double _Complex __pyx_t_double_complex;
+  #endif
+#else
+    typedef struct { double real, imag; } __pyx_t_double_complex;
+#endif
+
+
+/*--- Type declarations ---*/
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":765
+ * ctypedef npy_longdouble longdouble_t
+ * 
+ * ctypedef npy_cfloat      cfloat_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_cdouble     cdouble_t
+ * ctypedef npy_clongdouble clongdouble_t
+ */
+typedef npy_cfloat __pyx_t_5numpy_cfloat_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":766
+ * 
+ * ctypedef npy_cfloat      cfloat_t
+ * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_clongdouble clongdouble_t
+ * 
+ */
+typedef npy_cdouble __pyx_t_5numpy_cdouble_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":767
+ * ctypedef npy_cfloat      cfloat_t
+ * ctypedef npy_cdouble     cdouble_t
+ * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_cdouble     complex_t
+ */
+typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;
+
+/* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":769
+ * ctypedef npy_clongdouble clongdouble_t
+ * 
+ * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
+ * 
+ * cdef inline object PyArray_MultiIterNew1(a):
+ */
+typedef npy_cdouble __pyx_t_5numpy_complex_t;
+
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+  #define __Pyx_GOTREF(r)  __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
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+  #define __Pyx_XDECREF(r)  do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
+  #define __Pyx_XGOTREF(r)  do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
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+  #define __Pyx_RefNannyDeclarations
+  #define __Pyx_RefNannySetupContext(name, acquire_gil)
+  #define __Pyx_RefNannyFinishContext()
+  #define __Pyx_INCREF(r) Py_INCREF(r)
+  #define __Pyx_DECREF(r) Py_DECREF(r)
+  #define __Pyx_GOTREF(r)
+  #define __Pyx_GIVEREF(r)
+  #define __Pyx_XINCREF(r) Py_XINCREF(r)
+  #define __Pyx_XDECREF(r) Py_XDECREF(r)
+  #define __Pyx_XGOTREF(r)
+  #define __Pyx_XGIVEREF(r)
+#endif
+#define __Pyx_XDECREF_SET(r, v) do {                            \
+        PyObject *tmp = (PyObject *) r;                         \
+        r = v; __Pyx_XDECREF(tmp);                              \
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+#define __Pyx_DECREF_SET(r, v) do {                             \
+        PyObject *tmp = (PyObject *) r;                         \
+        r = v; __Pyx_DECREF(tmp);                               \
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+#define __Pyx_CLEAR(r)    do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
+#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
+    PyTypeObject* tp = Py_TYPE(obj);
+    if (likely(tp->tp_getattro))
+        return tp->tp_getattro(obj, attr_name);
+#if PY_MAJOR_VERSION < 3
+    if (likely(tp->tp_getattr))
+        return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
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+    return PyObject_GetAttr(obj, attr_name);
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+#else
+#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
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+static PyObject *__Pyx_GetBuiltinName(PyObject *name);
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+static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
+    Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
+
+static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
+
+static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[], \
+    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args, \
+    const char* function_name);
+
+static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
+    const char *name, int exact);
+
+static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
+#else
+#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
+#endif
+
+static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);
+
+static CYTHON_INLINE int  __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
+    __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
+static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
+
+static CYTHON_INLINE int __Pyx_IterFinish(void);
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
+#endif
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
+#else
+#define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
+#endif
+
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
+
+static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name);
+
+static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);
+
+static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);
+
+static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected);
+
+static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);
+
+static void __Pyx_UnpackTupleError(PyObject *, Py_ssize_t index);
+
+static CYTHON_INLINE int __Pyx_unpack_tuple2(PyObject* tuple, PyObject** value1, PyObject** value2,
+                                             int is_tuple, int has_known_size, int decref_tuple);
+
+static CYTHON_INLINE PyObject* __Pyx_dict_iterator(PyObject* dict, int is_dict, PyObject* method_name,
+                                                   Py_ssize_t* p_orig_length, int* p_is_dict);
+static CYTHON_INLINE int __Pyx_dict_iter_next(PyObject* dict_or_iter, Py_ssize_t orig_length, Py_ssize_t* ppos,
+                                              PyObject** pkey, PyObject** pvalue, PyObject** pitem, int is_dict);
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
+    PyListObject* L = (PyListObject*) list;
+    Py_ssize_t len = Py_SIZE(list);
+    if (likely(L->allocated > len)) {
+        Py_INCREF(x);
+        PyList_SET_ITEM(list, len, x);
+        Py_SIZE(list) = len+1;
+        return 0;
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+    return PyList_Append(list, x);
+}
+#else
+#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x)
+#endif
+
+#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0)
+static double __Pyx__PyObject_AsDouble(PyObject* obj);
+#if CYTHON_COMPILING_IN_PYPY
+#define __Pyx_PyObject_AsDouble(obj) \
+(likely(PyFloat_CheckExact(obj)) ? PyFloat_AS_DOUBLE(obj) : \
+ likely(PyInt_CheckExact(obj)) ? \
+ PyFloat_AsDouble(obj) : __Pyx__PyObject_AsDouble(obj))
+#else
+#define __Pyx_PyObject_AsDouble(obj) \
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+ PyFloat_AS_DOUBLE(obj) : __Pyx__PyObject_AsDouble(obj))
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+
+#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck) \
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+    __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) : \
+    (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) : \
+               __Pyx_GetItemInt_Generic(o, to_py_func(i))))
+#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck) \
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ? \
+    __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) : \
+    (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck);
+#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck) \
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ? \
+    __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) : \
+    (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck);
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
+                                                     int is_list, int wraparound, int boundscheck);
+
+static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb);
+static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb);
+
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
+
+#if PY_MAJOR_VERSION >= 3
+static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {
+    PyObject *value;
+    value = PyDict_GetItemWithError(d, key);
+    if (unlikely(!value)) {
+        if (!PyErr_Occurred()) {
+            PyObject* args = PyTuple_Pack(1, key);
+            if (likely(args))
+                PyErr_SetObject(PyExc_KeyError, args);
+            Py_XDECREF(args);
+        }
+        return NULL;
+    }
+    Py_INCREF(value);
+    return value;
+}
+#else
+    #define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key)
+#endif
+
+typedef struct {
+    int code_line;
+    PyCodeObject* code_object;
+} __Pyx_CodeObjectCacheEntry;
+struct __Pyx_CodeObjectCache {
+    int count;
+    int max_count;
+    __Pyx_CodeObjectCacheEntry* entries;
+};
+static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
+static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
+static PyCodeObject *__pyx_find_code_object(int code_line);
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
+
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename);
+
+typedef struct {
+  Py_ssize_t shape, strides, suboffsets;
+} __Pyx_Buf_DimInfo;
+typedef struct {
+  size_t refcount;
+  Py_buffer pybuffer;
+} __Pyx_Buffer;
+typedef struct {
+  __Pyx_Buffer *rcbuffer;
+  char *data;
+  __Pyx_Buf_DimInfo diminfo[8];
+} __Pyx_LocalBuf_ND;
+
+#if PY_MAJOR_VERSION < 3
+    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
+    static void __Pyx_ReleaseBuffer(Py_buffer *view);
+#else
+    #define __Pyx_GetBuffer PyObject_GetBuffer
+    #define __Pyx_ReleaseBuffer PyBuffer_Release
+#endif
+
+
+static Py_ssize_t __Pyx_zeros[] = {0, 0, 0, 0, 0, 0, 0, 0};
+static Py_ssize_t __Pyx_minusones[] = {-1, -1, -1, -1, -1, -1, -1, -1};
+
+static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
+
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
+
+static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
+
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #define __Pyx_CREAL(z) ((z).real())
+    #define __Pyx_CIMAG(z) ((z).imag())
+  #else
+    #define __Pyx_CREAL(z) (__real__(z))
+    #define __Pyx_CIMAG(z) (__imag__(z))
+  #endif
+#else
+    #define __Pyx_CREAL(z) ((z).real)
+    #define __Pyx_CIMAG(z) ((z).imag)
+#endif
+#if (defined(_WIN32) || defined(__clang__)) && defined(__cplusplus) && CYTHON_CCOMPLEX
+    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
+    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
+#else
+    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
+    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
+#endif
+
+static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);
+
+#if CYTHON_CCOMPLEX
+    #define __Pyx_c_eqf(a, b)   ((a)==(b))
+    #define __Pyx_c_sumf(a, b)  ((a)+(b))
+    #define __Pyx_c_difff(a, b) ((a)-(b))
+    #define __Pyx_c_prodf(a, b) ((a)*(b))
+    #define __Pyx_c_quotf(a, b) ((a)/(b))
+    #define __Pyx_c_negf(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zerof(z) ((z)==(float)0)
+    #define __Pyx_c_conjf(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_absf(z)     (::std::abs(z))
+        #define __Pyx_c_powf(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zerof(z) ((z)==0)
+    #define __Pyx_c_conjf(z)    (conjf(z))
+    #if 1
+        #define __Pyx_c_absf(z)     (cabsf(z))
+        #define __Pyx_c_powf(a, b)  (cpowf(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex);
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex);
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_powf(__pyx_t_float_complex, __pyx_t_float_complex);
+    #endif
+#endif
+
+static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);
+
+#if CYTHON_CCOMPLEX
+    #define __Pyx_c_eq(a, b)   ((a)==(b))
+    #define __Pyx_c_sum(a, b)  ((a)+(b))
+    #define __Pyx_c_diff(a, b) ((a)-(b))
+    #define __Pyx_c_prod(a, b) ((a)*(b))
+    #define __Pyx_c_quot(a, b) ((a)/(b))
+    #define __Pyx_c_neg(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero(z) ((z)==(double)0)
+    #define __Pyx_c_conj(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs(z)     (::std::abs(z))
+        #define __Pyx_c_pow(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero(z) ((z)==0)
+    #define __Pyx_c_conj(z)    (conj(z))
+    #if 1
+        #define __Pyx_c_abs(z)     (cabs(z))
+        #define __Pyx_c_pow(a, b)  (cpow(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex);
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex);
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex, __pyx_t_double_complex);
+    #endif
+#endif
+
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
+
+static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
+
+static int __Pyx_check_binary_version(void);
+
+#if !defined(__Pyx_PyIdentifier_FromString)
+#if PY_MAJOR_VERSION < 3
+  #define __Pyx_PyIdentifier_FromString(s) PyString_FromString(s)
+#else
+  #define __Pyx_PyIdentifier_FromString(s) PyUnicode_FromString(s)
+#endif
+#endif
+
+static PyObject *__Pyx_ImportModule(const char *name);
+
+static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict);
+
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
+
+
+/* Module declarations from 'cpython.buffer' */
+
+/* Module declarations from 'cpython.ref' */
+
+/* Module declarations from 'libc.string' */
+
+/* Module declarations from 'libc.stdio' */
+
+/* Module declarations from 'cpython.object' */
+
+/* Module declarations from '__builtin__' */
+
+/* Module declarations from 'cpython.type' */
+static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;
+
+/* Module declarations from 'libc.stdlib' */
+
+/* Module declarations from 'numpy' */
+
+/* Module declarations from 'numpy' */
+static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
+static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
+static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
+static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
+static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
+static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/
+
+/* Module declarations from 'libc.math' */
+
+/* Module declarations from 'ml3' */
+static __pyx_t_3ml3_DTYPE_t __pyx_f_3ml3_weight_success(int, int, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t); /*proto*/
+static __pyx_t_3ml3_DTYPE_t __pyx_f_3ml3_weight_failure(int, int, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t, __pyx_t_3ml3_DTYPE_t); /*proto*/
+static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_3ml3_DTYPE_t = { "DTYPE_t", NULL, sizeof(__pyx_t_3ml3_DTYPE_t), { 0 }, 0, 'R', 0, 0 };
+#define __Pyx_MODULE_NAME "ml3"
+int __pyx_module_is_main_ml3 = 0;
+
+/* Implementation of 'ml3' */
+static PyObject *__pyx_builtin_enumerate;
+static PyObject *__pyx_builtin_sum;
+static PyObject *__pyx_builtin_ValueError;
+static PyObject *__pyx_builtin_range;
+static PyObject *__pyx_builtin_RuntimeError;
+static PyObject *__pyx_pf_3ml3_ml3(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_root_victims, PyObject *__pyx_v_victims, CYTHON_UNUSED PyObject *__pyx_v_non_victims, CYTHON_UNUSED __pyx_t_3ml3_DTYPE_t __pyx_v_age, __pyx_t_3ml3_DTYPE_t __pyx_v_alpha, __pyx_t_3ml3_DTYPE_t __pyx_v_delta); /* proto */
+static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
+static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
+static char __pyx_k_B[] = "B";
+static char __pyx_k_H[] = "H";
+static char __pyx_k_I[] = "I";
+static char __pyx_k_L[] = "L";
+static char __pyx_k_O[] = "O";
+static char __pyx_k_Q[] = "Q";
+static char __pyx_k_b[] = "b";
+static char __pyx_k_d[] = "d";
+static char __pyx_k_f[] = "f";
+static char __pyx_k_g[] = "g";
+static char __pyx_k_h[] = "h";
+static char __pyx_k_i[] = "i";
+static char __pyx_k_l[] = "l";
+static char __pyx_k_q[] = "q";
+static char __pyx_k_s[] = "s";
+static char __pyx_k_t[] = "t";
+static char __pyx_k_Zd[] = "Zd";
+static char __pyx_k_Zf[] = "Zf";
+static char __pyx_k_Zg[] = "Zg";
+static char __pyx_k_dt[] = "dt";
+static char __pyx_k_ll[] = "ll";
+static char __pyx_k_np[] = "np";
+static char __pyx_k_w1[] = "w1";
+static char __pyx_k_w2[] = "w2";
+static char __pyx_k_w3[] = "w3";
+static char __pyx_k_age[] = "age";
+static char __pyx_k_dts[] = "dts";
+static char __pyx_k_inf[] = "-inf";
+static char __pyx_k_ml3[] = "ml3";
+static char __pyx_k_sum[] = "sum";
+static char __pyx_k_beta[] = "beta";
+static char __pyx_k_dist[] = "dist";
+static char __pyx_k_main[] = "__main__";
+static char __pyx_k_prnt[] = "prnt";
+static char __pyx_k_prob[] = "prob";
+static char __pyx_k_test[] = "__test__";
+static char __pyx_k_DTYPE[] = "DTYPE";
+static char __pyx_k_alpha[] = "alpha";
+static char __pyx_k_delta[] = "delta";
+static char __pyx_k_dists[] = "dists";
+static char __pyx_k_dtype[] = "dtype";
+static char __pyx_k_numpy[] = "numpy";
+static char __pyx_k_probs[] = "probs";
+static char __pyx_k_range[] = "range";
+static char __pyx_k_roots[] = "roots";
+static char __pyx_k_seeds[] = "seeds";
+static char __pyx_k_zeros[] = "zeros";
+static char __pyx_k_arange[] = "arange";
+static char __pyx_k_import[] = "__import__";
+static char __pyx_k_thresh[] = "thresh";
+static char __pyx_k_float64[] = "float64";
+static char __pyx_k_n_roots[] = "n_roots";
+static char __pyx_k_parents[] = "parents";
+static char __pyx_k_victims[] = "victims";
+static char __pyx_k_beta_add[] = "beta_add";
+static char __pyx_k_failures[] = "failures";
+static char __pyx_k_max_beta[] = "max_beta";
+static char __pyx_k_enumerate[] = "enumerate";
+static char __pyx_k_max_roots[] = "max_roots";
+static char __pyx_k_n_victims[] = "n_victims";
+static char __pyx_k_non_seeds[] = "non_seeds";
+static char __pyx_k_successes[] = "successes";
+static char __pyx_k_ValueError[] = "ValueError";
+static char __pyx_k_itervalues[] = "itervalues";
+static char __pyx_k_parent_dts[] = "parent_dts";
+static char __pyx_k_probs_fail[] = "probs_fail";
+static char __pyx_k_non_victims[] = "non_victims";
+static char __pyx_k_RuntimeError[] = "RuntimeError";
+static char __pyx_k_max_beta_add[] = "max_beta_add";
+static char __pyx_k_parent_dists[] = "parent_dists";
+static char __pyx_k_root_victims[] = "root_victims";
+static char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
+static char __pyx_k_Users_ben_Documents_Cascade_Pro[] = "/Users/ben/Documents/Cascade Project/criminal_cascades/experiments/ml3.pyx";
+static char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
+static char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
+static char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
+static char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
+static char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
+static PyObject *__pyx_n_s_DTYPE;
+static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
+static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
+static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
+static PyObject *__pyx_n_s_RuntimeError;
+static PyObject *__pyx_kp_s_Users_ben_Documents_Cascade_Pro;
+static PyObject *__pyx_n_s_ValueError;
+static PyObject *__pyx_n_s_age;
+static PyObject *__pyx_n_s_alpha;
+static PyObject *__pyx_n_s_arange;
+static PyObject *__pyx_n_s_beta;
+static PyObject *__pyx_n_s_beta_add;
+static PyObject *__pyx_n_s_delta;
+static PyObject *__pyx_n_s_dist;
+static PyObject *__pyx_n_s_dists;
+static PyObject *__pyx_n_s_dt;
+static PyObject *__pyx_n_s_dts;
+static PyObject *__pyx_n_s_dtype;
+static PyObject *__pyx_n_s_enumerate;
+static PyObject *__pyx_n_s_failures;
+static PyObject *__pyx_n_s_float64;
+static PyObject *__pyx_n_s_i;
+static PyObject *__pyx_n_s_import;
+static PyObject *__pyx_kp_s_inf;
+static PyObject *__pyx_n_s_itervalues;
+static PyObject *__pyx_n_s_l;
+static PyObject *__pyx_n_s_ll;
+static PyObject *__pyx_n_s_main;
+static PyObject *__pyx_n_s_max_beta;
+static PyObject *__pyx_n_s_max_beta_add;
+static PyObject *__pyx_n_s_max_roots;
+static PyObject *__pyx_n_s_ml3;
+static PyObject *__pyx_n_s_n_roots;
+static PyObject *__pyx_n_s_n_victims;
+static PyObject *__pyx_kp_u_ndarray_is_not_C_contiguous;
+static PyObject *__pyx_kp_u_ndarray_is_not_Fortran_contiguou;
+static PyObject *__pyx_n_s_non_seeds;
+static PyObject *__pyx_n_s_non_victims;
+static PyObject *__pyx_n_s_np;
+static PyObject *__pyx_n_s_numpy;
+static PyObject *__pyx_n_s_parent_dists;
+static PyObject *__pyx_n_s_parent_dts;
+static PyObject *__pyx_n_s_parents;
+static PyObject *__pyx_n_s_prnt;
+static PyObject *__pyx_n_s_prob;
+static PyObject *__pyx_n_s_probs;
+static PyObject *__pyx_n_s_probs_fail;
+static PyObject *__pyx_n_s_range;
+static PyObject *__pyx_n_s_root_victims;
+static PyObject *__pyx_n_s_roots;
+static PyObject *__pyx_n_s_s;
+static PyObject *__pyx_n_s_seeds;
+static PyObject *__pyx_n_s_successes;
+static PyObject *__pyx_n_s_sum;
+static PyObject *__pyx_n_s_t;
+static PyObject *__pyx_n_s_test;
+static PyObject *__pyx_n_s_thresh;
+static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
+static PyObject *__pyx_n_s_victims;
+static PyObject *__pyx_n_s_w1;
+static PyObject *__pyx_n_s_w2;
+static PyObject *__pyx_n_s_w3;
+static PyObject *__pyx_n_s_zeros;
+static PyObject *__pyx_float__01;
+static PyObject *__pyx_float_0_01;
+static PyObject *__pyx_int_1;
+static PyObject *__pyx_tuple_;
+static PyObject *__pyx_tuple__2;
+static PyObject *__pyx_tuple__3;
+static PyObject *__pyx_tuple__4;
+static PyObject *__pyx_tuple__5;
+static PyObject *__pyx_tuple__6;
+static PyObject *__pyx_tuple__7;
+static PyObject *__pyx_tuple__8;
+static PyObject *__pyx_codeobj__9;
+
+/* "ml3.pyx":9
+ * ctypedef np.float_t DTYPE_t
+ * 
+ * cdef DTYPE_t weight_success(int dist, int dt, DTYPE_t alpha, DTYPE_t delta,             # <<<<<<<<<<<<<<
+ *                             DTYPE_t w1, DTYPE_t w2, DTYPE_t w3):
+ *     """weight for successful infection, exponential time model"""
+ */
+
+static __pyx_t_3ml3_DTYPE_t __pyx_f_3ml3_weight_success(int __pyx_v_dist, int __pyx_v_dt, __pyx_t_3ml3_DTYPE_t __pyx_v_alpha, __pyx_t_3ml3_DTYPE_t __pyx_v_delta, CYTHON_UNUSED __pyx_t_3ml3_DTYPE_t __pyx_v_w1, CYTHON_UNUSED __pyx_t_3ml3_DTYPE_t __pyx_v_w2, CYTHON_UNUSED __pyx_t_3ml3_DTYPE_t __pyx_v_w3) {
+  __pyx_t_3ml3_DTYPE_t __pyx_v_structural;
+  __pyx_t_3ml3_DTYPE_t __pyx_v_temporal;
+  __pyx_t_3ml3_DTYPE_t __pyx_v_result;
+  __pyx_t_3ml3_DTYPE_t __pyx_r;
+  __Pyx_RefNannyDeclarations
+  __Pyx_RefNannySetupContext("weight_success", 0);
+
+  /* "ml3.pyx":13
+ *     """weight for successful infection, exponential time model"""
+ *     cdef DTYPE_t structural, temporal, result
+ *     structural = delta ** dist             # <<<<<<<<<<<<<<
+ *     temporal = log(exp(alpha)-1.) - alpha*dt
+ *     result = log(structural) + temporal
+ */
+  __pyx_v_structural = pow(__pyx_v_delta, ((__pyx_t_3ml3_DTYPE_t)__pyx_v_dist));
+
+  /* "ml3.pyx":14
+ *     cdef DTYPE_t structural, temporal, result
+ *     structural = delta ** dist
+ *     temporal = log(exp(alpha)-1.) - alpha*dt             # <<<<<<<<<<<<<<
+ *     result = log(structural) + temporal
+ *     return result
+ */
+  __pyx_v_temporal = (log((exp(__pyx_v_alpha) - 1.)) - (__pyx_v_alpha * __pyx_v_dt));
+
+  /* "ml3.pyx":15
+ *     structural = delta ** dist
+ *     temporal = log(exp(alpha)-1.) - alpha*dt
+ *     result = log(structural) + temporal             # <<<<<<<<<<<<<<
+ *     return result
+ * 
+ */
+  __pyx_v_result = (log(__pyx_v_structural) + __pyx_v_temporal);
+
+  /* "ml3.pyx":16
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+  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_float64); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+  __Pyx_GOTREF(__pyx_t_2);
+  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
+  if (PyDict_SetItem(__pyx_d, __pyx_n_s_DTYPE, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
+
+  /* "ml3.pyx":27
+ *     return result
+ * 
+ * def ml3(dict root_victims, dict victims, dict non_victims, DTYPE_t age,             # <<<<<<<<<<<<<<
+ *        DTYPE_t alpha, DTYPE_t delta):
+ *     cdef:
+ */
+  __pyx_t_2 = PyCFunction_NewEx(&__pyx_mdef_3ml3_1ml3, NULL, __pyx_n_s_ml3); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 27; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+  __Pyx_GOTREF(__pyx_t_2);
+  if (PyDict_SetItem(__pyx_d, __pyx_n_s_ml3, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 27; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
+
+  /* "ml3.pyx":1
+ * # cython: boundscheck=False, cdivision=True             # <<<<<<<<<<<<<<
+ * import numpy as np
+ * cimport numpy as np
+ */
+  __pyx_t_2 = PyDict_New(); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+  __Pyx_GOTREF(__pyx_t_2);
+  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
+
+  /* "../../../../Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":979
+ *      arr.base = baseptr
+ * 
+ * cdef inline object get_array_base(ndarray arr):             # <<<<<<<<<<<<<<
+ *     if arr.base is NULL:
+ *         return None
+ */
+
+  /*--- Wrapped vars code ---*/
+
+  goto __pyx_L0;
+  __pyx_L1_error:;
+  __Pyx_XDECREF(__pyx_t_1);
+  __Pyx_XDECREF(__pyx_t_2);
+  if (__pyx_m) {
+    if (__pyx_d) {
+      __Pyx_AddTraceback("init ml3", __pyx_clineno, __pyx_lineno, __pyx_filename);
+    }
+    Py_DECREF(__pyx_m); __pyx_m = 0;
+  } else if (!PyErr_Occurred()) {
+    PyErr_SetString(PyExc_ImportError, "init ml3");
+  }
+  __pyx_L0:;
+  __Pyx_RefNannyFinishContext();
+  #if PY_MAJOR_VERSION < 3
+  return;
+  #else
+  return __pyx_m;
+  #endif
+}
+
+/* --- Runtime support code --- */
+#if CYTHON_REFNANNY
+static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
+    PyObject *m = NULL, *p = NULL;
+    void *r = NULL;
+    m = PyImport_ImportModule((char *)modname);
+    if (!m) goto end;
+    p = PyObject_GetAttrString(m, (char *)"RefNannyAPI");
+    if (!p) goto end;
+    r = PyLong_AsVoidPtr(p);
+end:
+    Py_XDECREF(p);
+    Py_XDECREF(m);
+    return (__Pyx_RefNannyAPIStruct *)r;
+}
+#endif
+
+static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
+    PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
+    if (unlikely(!result)) {
+        PyErr_Format(PyExc_NameError,
+#if PY_MAJOR_VERSION >= 3
+            "name '%U' is not defined", name);
+#else
+            "name '%.200s' is not defined", PyString_AS_STRING(name));
+#endif
+    }
+    return result;
+}
+
+static void __Pyx_RaiseArgtupleInvalid(
+    const char* func_name,
+    int exact,
+    Py_ssize_t num_min,
+    Py_ssize_t num_max,
+    Py_ssize_t num_found)
+{
+    Py_ssize_t num_expected;
+    const char *more_or_less;
+    if (num_found < num_min) {
+        num_expected = num_min;
+        more_or_less = "at least";
+    } else {
+        num_expected = num_max;
+        more_or_less = "at most";
+    }
+    if (exact) {
+        more_or_less = "exactly";
+    }
+    PyErr_Format(PyExc_TypeError,
+                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                 func_name, more_or_less, num_expected,
+                 (num_expected == 1) ? "" : "s", num_found);
+}
+
+static void __Pyx_RaiseDoubleKeywordsError(
+    const char* func_name,
+    PyObject* kw_name)
+{
+    PyErr_Format(PyExc_TypeError,
+        #if PY_MAJOR_VERSION >= 3
+        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
+        #else
+        "%s() got multiple values for keyword argument '%s'", func_name,
+        PyString_AsString(kw_name));
+        #endif
+}
+
+static int __Pyx_ParseOptionalKeywords(
+    PyObject *kwds,
+    PyObject **argnames[],
+    PyObject *kwds2,
+    PyObject *values[],
+    Py_ssize_t num_pos_args,
+    const char* function_name)
+{
+    PyObject *key = 0, *value = 0;
+    Py_ssize_t pos = 0;
+    PyObject*** name;
+    PyObject*** first_kw_arg = argnames + num_pos_args;
+    while (PyDict_Next(kwds, &pos, &key, &value)) {
+        name = first_kw_arg;
+        while (*name && (**name != key)) name++;
+        if (*name) {
+            values[name-argnames] = value;
+            continue;
+        }
+        name = first_kw_arg;
+        #if PY_MAJOR_VERSION < 3
+        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
+            while (*name) {
+                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
+                        && _PyString_Eq(**name, key)) {
+                    values[name-argnames] = value;
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    if ((**argname == key) || (
+                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
+                             && _PyString_Eq(**argname, key))) {
+                        goto arg_passed_twice;
+                    }
+                    argname++;
+                }
+            }
+        } else
+        #endif
+        if (likely(PyUnicode_Check(key))) {
+            while (*name) {
+                int cmp = (**name == key) ? 0 :
+                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
+                #endif
+                    PyUnicode_Compare(**name, key);
+                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                if (cmp == 0) {
+                    values[name-argnames] = value;
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    int cmp = (**argname == key) ? 0 :
+                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
+                    #endif
+                        PyUnicode_Compare(**argname, key);
+                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                    if (cmp == 0) goto arg_passed_twice;
+                    argname++;
+                }
+            }
+        } else
+            goto invalid_keyword_type;
+        if (kwds2) {
+            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
+        } else {
+            goto invalid_keyword;
+        }
+    }
+    return 0;
+arg_passed_twice:
+    __Pyx_RaiseDoubleKeywordsError(function_name, key);
+    goto bad;
+invalid_keyword_type:
+    PyErr_Format(PyExc_TypeError,
+        "%.200s() keywords must be strings", function_name);
+    goto bad;
+invalid_keyword:
+    PyErr_Format(PyExc_TypeError,
+    #if PY_MAJOR_VERSION < 3
+        "%.200s() got an unexpected keyword argument '%.200s'",
+        function_name, PyString_AsString(key));
+    #else
+        "%s() got an unexpected keyword argument '%U'",
+        function_name, key);
+    #endif
+bad:
+    return -1;
+}
+
+static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
+    PyErr_Format(PyExc_TypeError,
+        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
+        name, type->tp_name, Py_TYPE(obj)->tp_name);
+}
+static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
+    const char *name, int exact)
+{
+    if (unlikely(!type)) {
+        PyErr_SetString(PyExc_SystemError, "Missing type object");
+        return 0;
+    }
+    if (none_allowed && obj == Py_None) return 1;
+    else if (exact) {
+        if (likely(Py_TYPE(obj) == type)) return 1;
+        #if PY_MAJOR_VERSION == 2
+        else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
+        #endif
+    }
+    else {
+        if (likely(PyObject_TypeCheck(obj, type))) return 1;
+    }
+    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
+    return 0;
+}
+
+static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
+    PyObject *result;
+#if CYTHON_COMPILING_IN_CPYTHON
+    result = PyDict_GetItem(__pyx_d, name);
+    if (likely(result)) {
+        Py_INCREF(result);
+    } else {
+#else
+    result = PyObject_GetItem(__pyx_d, name);
+    if (!result) {
+        PyErr_Clear();
+#endif
+        result = __Pyx_GetBuiltinName(name);
+    }
+    return result;
+}
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
+    PyObject *result;
+    ternaryfunc call = func->ob_type->tp_call;
+    if (unlikely(!call))
+        return PyObject_Call(func, arg, kw);
+    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
+        return NULL;
+    result = (*call)(func, arg, kw);
+    Py_LeaveRecursiveCall();
+    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
+        PyErr_SetString(
+            PyExc_SystemError,
+            "NULL result without error in PyObject_Call");
+    }
+    return result;
+}
+#endif
+
+static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
+    if (unlikely(!type)) {
+        PyErr_SetString(PyExc_SystemError, "Missing type object");
+        return 0;
+    }
+    if (likely(PyObject_TypeCheck(obj, type)))
+        return 1;
+    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
+                 Py_TYPE(obj)->tp_name, type->tp_name);
+    return 0;
+}
+
+static CYTHON_INLINE int __Pyx_IsLittleEndian(void) {
+  unsigned int n = 1;
+  return *(unsigned char*)(&n) != 0;
+}
+static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
+                              __Pyx_BufFmt_StackElem* stack,
+                              __Pyx_TypeInfo* type) {
+  stack[0].field = &ctx->root;
+  stack[0].parent_offset = 0;
+  ctx->root.type = type;
+  ctx->root.name = "buffer dtype";
+  ctx->root.offset = 0;
+  ctx->head = stack;
+  ctx->head->field = &ctx->root;
+  ctx->fmt_offset = 0;
+  ctx->head->parent_offset = 0;
+  ctx->new_packmode = '@';
+  ctx->enc_packmode = '@';
+  ctx->new_count = 1;
+  ctx->enc_count = 0;
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  ctx->is_valid_array = 0;
+  ctx->struct_alignment = 0;
+  while (type->typegroup == 'S') {
+    ++ctx->head;
+    ctx->head->field = type->fields;
+    ctx->head->parent_offset = 0;
+    type = type->fields->type;
+  }
+}
+static int __Pyx_BufFmt_ParseNumber(const char** ts) {
+    int count;
+    const char* t = *ts;
+    if (*t < '0' || *t > '9') {
+      return -1;
+    } else {
+        count = *t++ - '0';
+        while (*t >= '0' && *t < '9') {
+            count *= 10;
+            count += *t++ - '0';
+        }
+    }
+    *ts = t;
+    return count;
+}
+static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
+    int number = __Pyx_BufFmt_ParseNumber(ts);
+    if (number == -1)
+        PyErr_Format(PyExc_ValueError,\
+                     "Does not understand character buffer dtype format string ('%c')", **ts);
+    return number;
+}
+static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
+  PyErr_Format(PyExc_ValueError,
+               "Unexpected format string character: '%c'", ch);
+}
+static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
+  switch (ch) {
+    case 'c': return "'char'";
+    case 'b': return "'signed char'";
+    case 'B': return "'unsigned char'";
+    case 'h': return "'short'";
+    case 'H': return "'unsigned short'";
+    case 'i': return "'int'";
+    case 'I': return "'unsigned int'";
+    case 'l': return "'long'";
+    case 'L': return "'unsigned long'";
+    case 'q': return "'long long'";
+    case 'Q': return "'unsigned long long'";
+    case 'f': return (is_complex ? "'complex float'" : "'float'");
+    case 'd': return (is_complex ? "'complex double'" : "'double'");
+    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
+    case 'T': return "a struct";
+    case 'O': return "Python object";
+    case 'P': return "a pointer";
+    case 's': case 'p': return "a string";
+    case 0: return "end";
+    default: return "unparseable format string";
+  }
+}
+static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return 2;
+    case 'i': case 'I': case 'l': case 'L': return 4;
+    case 'q': case 'Q': return 8;
+    case 'f': return (is_complex ? 8 : 4);
+    case 'd': return (is_complex ? 16 : 8);
+    case 'g': {
+      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
+      return 0;
+    }
+    case 'O': case 'P': return sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
+  switch (ch) {
+    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(short);
+    case 'i': case 'I': return sizeof(int);
+    case 'l': case 'L': return sizeof(long);
+    #ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
+    #endif
+    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
+    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
+    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
+    case 'O': case 'P': return sizeof(void*);
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+typedef struct { char c; short x; } __Pyx_st_short;
+typedef struct { char c; int x; } __Pyx_st_int;
+typedef struct { char c; long x; } __Pyx_st_long;
+typedef struct { char c; float x; } __Pyx_st_float;
+typedef struct { char c; double x; } __Pyx_st_double;
+typedef struct { char c; long double x; } __Pyx_st_longdouble;
+typedef struct { char c; void *x; } __Pyx_st_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+/* These are for computing the padding at the end of the struct to align
+   on the first member of the struct. This will probably the same as above,
+   but we don't have any guarantees.
+ */
+typedef struct { short x; char c; } __Pyx_pad_short;
+typedef struct { int x; char c; } __Pyx_pad_int;
+typedef struct { long x; char c; } __Pyx_pad_long;
+typedef struct { float x; char c; } __Pyx_pad_float;
+typedef struct { double x; char c; } __Pyx_pad_double;
+typedef struct { long double x; char c; } __Pyx_pad_longdouble;
+typedef struct { void *x; char c; } __Pyx_pad_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
+  switch (ch) {
+    case 'c':
+        return 'H';
+    case 'b': case 'h': case 'i':
+    case 'l': case 'q': case 's': case 'p':
+        return 'I';
+    case 'B': case 'H': case 'I': case 'L': case 'Q':
+        return 'U';
+    case 'f': case 'd': case 'g':
+        return (is_complex ? 'C' : 'R');
+    case 'O':
+        return 'O';
+    case 'P':
+        return 'P';
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
+  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
+    const char* expected;
+    const char* quote;
+    if (ctx->head == NULL) {
+      expected = "end";
+      quote = "";
+    } else {
+      expected = ctx->head->field->type->name;
+      quote = "'";
+    }
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected %s%s%s but got %s",
+                 quote, expected, quote,
+                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
+  } else {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_StructField* parent = (ctx->head - 1)->field;
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
+                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
+                 parent->type->name, field->name);
+  }
+}
+static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
+  char group;
+  size_t size, offset, arraysize = 1;
+  if (ctx->enc_type == 0) return 0;
+  if (ctx->head->field->type->arraysize[0]) {
+    int i, ndim = 0;
+    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
+        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
+        ndim = 1;
+        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
+            PyErr_Format(PyExc_ValueError,
+                         "Expected a dimension of size %zu, got %zu",
+                         ctx->head->field->type->arraysize[0], ctx->enc_count);
+            return -1;
+        }
+    }
+    if (!ctx->is_valid_array) {
+      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
+                   ctx->head->field->type->ndim, ndim);
+      return -1;
+    }
+    for (i = 0; i < ctx->head->field->type->ndim; i++) {
+      arraysize *= ctx->head->field->type->arraysize[i];
+    }
+    ctx->is_valid_array = 0;
+    ctx->enc_count = 1;
+  }
+  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
+  do {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_TypeInfo* type = field->type;
+    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
+      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
+    } else {
+      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
+    }
+    if (ctx->enc_packmode == '@') {
+      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
+      size_t align_mod_offset;
+      if (align_at == 0) return -1;
+      align_mod_offset = ctx->fmt_offset % align_at;
+      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
+      if (ctx->struct_alignment == 0)
+          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
+                                                                 ctx->is_complex);
+    }
+    if (type->size != size || type->typegroup != group) {
+      if (type->typegroup == 'C' && type->fields != NULL) {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        ++ctx->head;
+        ctx->head->field = type->fields;
+        ctx->head->parent_offset = parent_offset;
+        continue;
+      }
+      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
+      } else {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+      }
+    }
+    offset = ctx->head->parent_offset + field->offset;
+    if (ctx->fmt_offset != offset) {
+      PyErr_Format(PyExc_ValueError,
+                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
+                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
+      return -1;
+    }
+    ctx->fmt_offset += size;
+    if (arraysize)
+      ctx->fmt_offset += (arraysize - 1) * size;
+    --ctx->enc_count;
+    while (1) {
+      if (field == &ctx->root) {
+        ctx->head = NULL;
+        if (ctx->enc_count != 0) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+        }
+        break;
+      }
+      ctx->head->field = ++field;
+      if (field->type == NULL) {
+        --ctx->head;
+        field = ctx->head->field;
+        continue;
+      } else if (field->type->typegroup == 'S') {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        if (field->type->fields->type == NULL) continue;
+        field = field->type->fields;
+        ++ctx->head;
+        ctx->head->field = field;
+        ctx->head->parent_offset = parent_offset;
+        break;
+      } else {
+        break;
+      }
+    }
+  } while (ctx->enc_count);
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  return 0;
+}
+static CYTHON_INLINE PyObject *
+__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
+{
+    const char *ts = *tsp;
+    int i = 0, number;
+    int ndim = ctx->head->field->type->ndim;
+;
+    ++ts;
+    if (ctx->new_count != 1) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Cannot handle repeated arrays in format string");
+        return NULL;
+    }
+    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+    while (*ts && *ts != ')') {
+        switch (*ts) {
+            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
+            default:  break;
+        }
+        number = __Pyx_BufFmt_ExpectNumber(&ts);
+        if (number == -1) return NULL;
+        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
+            return PyErr_Format(PyExc_ValueError,
+                        "Expected a dimension of size %zu, got %d",
+                        ctx->head->field->type->arraysize[i], number);
+        if (*ts != ',' && *ts != ')')
+            return PyErr_Format(PyExc_ValueError,
+                                "Expected a comma in format string, got '%c'", *ts);
+        if (*ts == ',') ts++;
+        i++;
+    }
+    if (i != ndim)
+        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
+                            ctx->head->field->type->ndim, i);
+    if (!*ts) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Unexpected end of format string, expected ')'");
+        return NULL;
+    }
+    ctx->is_valid_array = 1;
+    ctx->new_count = 1;
+    *tsp = ++ts;
+    return Py_None;
+}
+static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
+  int got_Z = 0;
+  while (1) {
+    switch(*ts) {
+      case 0:
+        if (ctx->enc_type != 0 && ctx->head == NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        if (ctx->head != NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        return ts;
+      case ' ':
+      case '\r':
+      case '\n':
+        ++ts;
+        break;
+      case '<':
+        if (!__Pyx_IsLittleEndian()) {
+          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '>':
+      case '!':
+        if (__Pyx_IsLittleEndian()) {
+          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '=':
+      case '@':
+      case '^':
+        ctx->new_packmode = *ts++;
+        break;
+      case 'T':
+        {
+          const char* ts_after_sub;
+          size_t i, struct_count = ctx->new_count;
+          size_t struct_alignment = ctx->struct_alignment;
+          ctx->new_count = 1;
+          ++ts;
+          if (*ts != '{') {
+            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
+            return NULL;
+          }
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          ctx->enc_count = 0;
+          ctx->struct_alignment = 0;
+          ++ts;
+          ts_after_sub = ts;
+          for (i = 0; i != struct_count; ++i) {
+            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
+            if (!ts_after_sub) return NULL;
+          }
+          ts = ts_after_sub;
+          if (struct_alignment) ctx->struct_alignment = struct_alignment;
+        }
+        break;
+      case '}':
+        {
+          size_t alignment = ctx->struct_alignment;
+          ++ts;
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          if (alignment && ctx->fmt_offset % alignment) {
+            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
+          }
+        }
+        return ts;
+      case 'x':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->fmt_offset += ctx->new_count;
+        ctx->new_count = 1;
+        ctx->enc_count = 0;
+        ctx->enc_type = 0;
+        ctx->enc_packmode = ctx->new_packmode;
+        ++ts;
+        break;
+      case 'Z':
+        got_Z = 1;
+        ++ts;
+        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
+          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
+          return NULL;
+        }
+      case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
+      case 'l': case 'L': case 'q': case 'Q':
+      case 'f': case 'd': case 'g':
+      case 'O': case 'p':
+        if (ctx->enc_type == *ts && got_Z == ctx->is_complex &&
+            ctx->enc_packmode == ctx->new_packmode) {
+          ctx->enc_count += ctx->new_count;
+          ctx->new_count = 1;
+          got_Z = 0;
+          ++ts;
+          break;
+        }
+      case 's':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->enc_count = ctx->new_count;
+        ctx->enc_packmode = ctx->new_packmode;
+        ctx->enc_type = *ts;
+        ctx->is_complex = got_Z;
+        ++ts;
+        ctx->new_count = 1;
+        got_Z = 0;
+        break;
+      case ':':
+        ++ts;
+        while(*ts != ':') ++ts;
+        ++ts;
+        break;
+      case '(':
+        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
+        break;
+      default:
+        {
+          int number = __Pyx_BufFmt_ExpectNumber(&ts);
+          if (number == -1) return NULL;
+          ctx->new_count = (size_t)number;
+        }
+    }
+  }
+}
+static CYTHON_INLINE void __Pyx_ZeroBuffer(Py_buffer* buf) {
+  buf->buf = NULL;
+  buf->obj = NULL;
+  buf->strides = __Pyx_zeros;
+  buf->shape = __Pyx_zeros;
+  buf->suboffsets = __Pyx_minusones;
+}
+static CYTHON_INLINE int __Pyx_GetBufferAndValidate(
+        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
+        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
+{
+  if (obj == Py_None || obj == NULL) {
+    __Pyx_ZeroBuffer(buf);
+    return 0;
+  }
+  buf->buf = NULL;
+  if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail;
+  if (buf->ndim != nd) {
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer has wrong number of dimensions (expected %d, got %d)",
+                 nd, buf->ndim);
+    goto fail;
+  }
+  if (!cast) {
+    __Pyx_BufFmt_Context ctx;
+    __Pyx_BufFmt_Init(&ctx, stack, dtype);
+    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
+  }
+  if ((unsigned)buf->itemsize != dtype->size) {
+    PyErr_Format(PyExc_ValueError,
+      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
+      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
+      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
+    goto fail;
+  }
+  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
+  return 0;
+fail:;
+  __Pyx_ZeroBuffer(buf);
+  return -1;
+}
+static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
+  if (info->buf == NULL) return;
+  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
+  __Pyx_ReleaseBuffer(info);
+}
+
+static CYTHON_INLINE int __Pyx_IterFinish(void) {
+#if CYTHON_COMPILING_IN_CPYTHON
+    PyThreadState *tstate = PyThreadState_GET();
+    PyObject* exc_type = tstate->curexc_type;
+    if (unlikely(exc_type)) {
+        if (likely(exc_type == PyExc_StopIteration) || PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration)) {
+            PyObject *exc_value, *exc_tb;
+            exc_value = tstate->curexc_value;
+            exc_tb = tstate->curexc_traceback;
+            tstate->curexc_type = 0;
+            tstate->curexc_value = 0;
+            tstate->curexc_traceback = 0;
+            Py_DECREF(exc_type);
+            Py_XDECREF(exc_value);
+            Py_XDECREF(exc_tb);
+            return 0;
+        } else {
+            return -1;
+        }
+    }
+    return 0;
+#else
+    if (unlikely(PyErr_Occurred())) {
+        if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) {
+            PyErr_Clear();
+            return 0;
+        } else {
+            return -1;
+        }
+    }
+    return 0;
+#endif
+}
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
+    PyObject *self, *result;
+    PyCFunction cfunc;
+    cfunc = PyCFunction_GET_FUNCTION(func);
+    self = PyCFunction_GET_SELF(func);
+    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
+        return NULL;
+    result = cfunc(self, arg);
+    Py_LeaveRecursiveCall();
+    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
+        PyErr_SetString(
+            PyExc_SystemError,
+            "NULL result without error in PyObject_Call");
+    }
+    return result;
+}
+#endif
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
+#ifdef __Pyx_CyFunction_USED
+    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
+#else
+    if (likely(PyCFunction_Check(func))) {
+#endif
+        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
+            return __Pyx_PyObject_CallMethO(func, NULL);
+        }
+    }
+    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
+}
+#endif
+
+#if CYTHON_COMPILING_IN_CPYTHON
+static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+    PyObject *result;
+    PyObject *args = PyTuple_New(1);
+    if (unlikely(!args)) return NULL;
+    Py_INCREF(arg);
+    PyTuple_SET_ITEM(args, 0, arg);
+    result = __Pyx_PyObject_Call(func, args, NULL);
+    Py_DECREF(args);
+    return result;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+#ifdef __Pyx_CyFunction_USED
+    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
+#else
+    if (likely(PyCFunction_Check(func))) {
+#endif
+        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
+            return __Pyx_PyObject_CallMethO(func, arg);
+        }
+    }
+    return __Pyx__PyObject_CallOneArg(func, arg);
+}
+#else
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+    PyObject* args = PyTuple_Pack(1, arg);
+    return (likely(args)) ? __Pyx_PyObject_Call(func, args, NULL) : NULL;
+}
+#endif
+
+static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name) {
+    PyObject *method, *result = NULL;
+    method = __Pyx_PyObject_GetAttrStr(obj, method_name);
+    if (unlikely(!method)) goto bad;
+#if CYTHON_COMPILING_IN_CPYTHON
+    if (likely(PyMethod_Check(method))) {
+        PyObject *self = PyMethod_GET_SELF(method);
+        if (likely(self)) {
+            PyObject *function = PyMethod_GET_FUNCTION(method);
+            result = __Pyx_PyObject_CallOneArg(function, self);
+            Py_DECREF(method);
+            return result;
+        }
+    }
+#endif
+    result = __Pyx_PyObject_CallNoArg(method);
+    Py_DECREF(method);
+bad:
+    return result;
+}
+
+static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
+    PyErr_Format(PyExc_ValueError,
+                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
+                 index, (index == 1) ? "" : "s");
+}
+
+static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
+    PyErr_Format(PyExc_ValueError,
+                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
+}
+
+static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
+    if (unlikely(retval)) {
+        Py_DECREF(retval);
+        __Pyx_RaiseTooManyValuesError(expected);
+        return -1;
+    } else {
+        return __Pyx_IterFinish();
+    }
+    return 0;
+}
+
+static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
+    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
+}
+
+static void __Pyx_UnpackTupleError(PyObject *t, Py_ssize_t index) {
+    if (t == Py_None) {
+      __Pyx_RaiseNoneNotIterableError();
+    } else if (PyTuple_GET_SIZE(t) < index) {
+      __Pyx_RaiseNeedMoreValuesError(PyTuple_GET_SIZE(t));
+    } else {
+      __Pyx_RaiseTooManyValuesError(index);
+    }
+}
+
+static CYTHON_INLINE int __Pyx_unpack_tuple2(PyObject* tuple, PyObject** pvalue1, PyObject** pvalue2,
+                                             int is_tuple, int has_known_size, int decref_tuple) {
+    Py_ssize_t index;
+    PyObject *value1 = NULL, *value2 = NULL, *iter = NULL;
+    if (!is_tuple && unlikely(!PyTuple_Check(tuple))) {
+        iternextfunc iternext;
+        iter = PyObject_GetIter(tuple);
+        if (unlikely(!iter)) goto bad;
+        if (decref_tuple) { Py_DECREF(tuple); tuple = NULL; }
+        iternext = Py_TYPE(iter)->tp_iternext;
+        value1 = iternext(iter); if (unlikely(!value1)) { index = 0; goto unpacking_failed; }
+        value2 = iternext(iter); if (unlikely(!value2)) { index = 1; goto unpacking_failed; }
+        if (!has_known_size && unlikely(__Pyx_IternextUnpackEndCheck(iternext(iter), 2))) goto bad;
+        Py_DECREF(iter);
+    } else {
+        if (!has_known_size && unlikely(PyTuple_GET_SIZE(tuple) != 2)) {
+            __Pyx_UnpackTupleError(tuple, 2);
+            goto bad;
+        }
+#if CYTHON_COMPILING_IN_PYPY
+        value1 = PySequence_ITEM(tuple, 0);
+        if (unlikely(!value1)) goto bad;
+        value2 = PySequence_ITEM(tuple, 1);
+        if (unlikely(!value2)) goto bad;
+#else
+        value1 = PyTuple_GET_ITEM(tuple, 0);
+        value2 = PyTuple_GET_ITEM(tuple, 1);
+        Py_INCREF(value1);
+        Py_INCREF(value2);
+#endif
+        if (decref_tuple) { Py_DECREF(tuple); }
+    }
+    *pvalue1 = value1;
+    *pvalue2 = value2;
+    return 0;
+unpacking_failed:
+    if (!has_known_size && __Pyx_IterFinish() == 0)
+        __Pyx_RaiseNeedMoreValuesError(index);
+bad:
+    Py_XDECREF(iter);
+    Py_XDECREF(value1);
+    Py_XDECREF(value2);
+    if (decref_tuple) { Py_XDECREF(tuple); }
+    return -1;
+}
+
+static CYTHON_INLINE PyObject* __Pyx_dict_iterator(PyObject* iterable, int is_dict, PyObject* method_name,
+                                                   Py_ssize_t* p_orig_length, int* p_source_is_dict) {
+    is_dict = is_dict || likely(PyDict_CheckExact(iterable));
+    *p_source_is_dict = is_dict;
+#if !CYTHON_COMPILING_IN_PYPY
+    if (is_dict) {
+        *p_orig_length = PyDict_Size(iterable);
+        Py_INCREF(iterable);
+        return iterable;
+    }
+#endif
+    *p_orig_length = 0;
+    if (method_name) {
+        PyObject* iter;
+        iterable = __Pyx_PyObject_CallMethod0(iterable, method_name);
+        if (!iterable)
+            return NULL;
+#if !CYTHON_COMPILING_IN_PYPY
+        if (PyTuple_CheckExact(iterable) || PyList_CheckExact(iterable))
+            return iterable;
+#endif
+        iter = PyObject_GetIter(iterable);
+        Py_DECREF(iterable);
+        return iter;
+    }
+    return PyObject_GetIter(iterable);
+}
+static CYTHON_INLINE int __Pyx_dict_iter_next(PyObject* iter_obj, Py_ssize_t orig_length, Py_ssize_t* ppos,
+                                              PyObject** pkey, PyObject** pvalue, PyObject** pitem, int source_is_dict) {
+    PyObject* next_item;
+#if !CYTHON_COMPILING_IN_PYPY
+    if (source_is_dict) {
+        PyObject *key, *value;
+        if (unlikely(orig_length != PyDict_Size(iter_obj))) {
+            PyErr_SetString(PyExc_RuntimeError, "dictionary changed size during iteration");
+            return -1;
+        }
+        if (unlikely(!PyDict_Next(iter_obj, ppos, &key, &value))) {
+            return 0;
+        }
+        if (pitem) {
+            PyObject* tuple = PyTuple_New(2);
+            if (unlikely(!tuple)) {
+                return -1;
+            }
+            Py_INCREF(key);
+            Py_INCREF(value);
+            PyTuple_SET_ITEM(tuple, 0, key);
+            PyTuple_SET_ITEM(tuple, 1, value);
+            *pitem = tuple;
+        } else {
+            if (pkey) {
+                Py_INCREF(key);
+                *pkey = key;
+            }
+            if (pvalue) {
+                Py_INCREF(value);
+                *pvalue = value;
+            }
+        }
+        return 1;
+    } else if (PyTuple_CheckExact(iter_obj)) {
+        Py_ssize_t pos = *ppos;
+        if (unlikely(pos >= PyTuple_GET_SIZE(iter_obj))) return 0;
+        *ppos = pos + 1;
+        next_item = PyTuple_GET_ITEM(iter_obj, pos);
+        Py_INCREF(next_item);
+    } else if (PyList_CheckExact(iter_obj)) {
+        Py_ssize_t pos = *ppos;
+        if (unlikely(pos >= PyList_GET_SIZE(iter_obj))) return 0;
+        *ppos = pos + 1;
+        next_item = PyList_GET_ITEM(iter_obj, pos);
+        Py_INCREF(next_item);
+    } else
+#endif
+    {
+        next_item = PyIter_Next(iter_obj);
+        if (unlikely(!next_item)) {
+            return __Pyx_IterFinish();
+        }
+    }
+    if (pitem) {
+        *pitem = next_item;
+    } else if (pkey && pvalue) {
+        if (__Pyx_unpack_tuple2(next_item, pkey, pvalue, source_is_dict, source_is_dict, 1))
+            return -1;
+    } else if (pkey) {
+        *pkey = next_item;
+    } else {
+        *pvalue = next_item;
+    }
+    return 1;
+}
+
+static double __Pyx__PyObject_AsDouble(PyObject* obj) {
+    PyObject* float_value;
+#if CYTHON_COMPILING_IN_PYPY
+    float_value = PyNumber_Float(obj);
+#else
+    PyNumberMethods *nb = Py_TYPE(obj)->tp_as_number;
+    if (likely(nb) && likely(nb->nb_float)) {
+        float_value = nb->nb_float(obj);
+        if (likely(float_value) && unlikely(!PyFloat_Check(float_value))) {
+            PyErr_Format(PyExc_TypeError,
+                "__float__ returned non-float (type %.200s)",
+                Py_TYPE(float_value)->tp_name);
+            Py_DECREF(float_value);
+            goto bad;
+        }
+    } else if (PyUnicode_CheckExact(obj) || PyBytes_CheckExact(obj)) {
+#if PY_MAJOR_VERSION >= 3
+        float_value = PyFloat_FromString(obj);
+#else
+        float_value = PyFloat_FromString(obj, 0);
+#endif
+    } else {
+        PyObject* args = PyTuple_New(1);
+        if (unlikely(!args)) goto bad;
+        PyTuple_SET_ITEM(args, 0, obj);
+        float_value = PyObject_Call((PyObject*)&PyFloat_Type, args, 0);
+        PyTuple_SET_ITEM(args, 0, 0);
+        Py_DECREF(args);
+    }
+#endif
+    if (likely(float_value)) {
+        double value = PyFloat_AS_DOUBLE(float_value);
+        Py_DECREF(float_value);
+        return value;
+    }
+bad:
+    return (double)-1;
+}
+
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
+    PyObject *r;
+    if (!j) return NULL;
+    r = PyObject_GetItem(o, j);
+    Py_DECREF(j);
+    return r;
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck) {
+#if CYTHON_COMPILING_IN_CPYTHON
+    if (wraparound & unlikely(i < 0)) i += PyList_GET_SIZE(o);
+    if ((!boundscheck) || likely((0 <= i) & (i < PyList_GET_SIZE(o)))) {
+        PyObject *r = PyList_GET_ITEM(o, i);
+        Py_INCREF(r);
+        return r;
+    }
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+#else
+    return PySequence_GetItem(o, i);
+#endif
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck) {
+#if CYTHON_COMPILING_IN_CPYTHON
+    if (wraparound & unlikely(i < 0)) i += PyTuple_GET_SIZE(o);
+    if ((!boundscheck) || likely((0 <= i) & (i < PyTuple_GET_SIZE(o)))) {
+        PyObject *r = PyTuple_GET_ITEM(o, i);
+        Py_INCREF(r);
+        return r;
+    }
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+#else
+    return PySequence_GetItem(o, i);
+#endif
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
+                                                     int is_list, int wraparound, int boundscheck) {
+#if CYTHON_COMPILING_IN_CPYTHON
+    if (is_list || PyList_CheckExact(o)) {
+        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
+        if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) {
+            PyObject *r = PyList_GET_ITEM(o, n);
+            Py_INCREF(r);
+            return r;
+        }
+    }
+    else if (PyTuple_CheckExact(o)) {
+        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
+        if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) {
+            PyObject *r = PyTuple_GET_ITEM(o, n);
+            Py_INCREF(r);
+            return r;
+        }
+    } else {
+        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
+        if (likely(m && m->sq_item)) {
+            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
+                Py_ssize_t l = m->sq_length(o);
+                if (likely(l >= 0)) {
+                    i += l;
+                } else {
+                    if (PyErr_ExceptionMatches(PyExc_OverflowError))
+                        PyErr_Clear();
+                    else
+                        return NULL;
+                }
+            }
+            return m->sq_item(o, i);
+        }
+    }
+#else
+    if (is_list || PySequence_Check(o)) {
+        return PySequence_GetItem(o, i);
+    }
+#endif
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+}
+
+static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
+#if CYTHON_COMPILING_IN_CPYTHON
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    PyThreadState *tstate = PyThreadState_GET();
+    tmp_type = tstate->curexc_type;
+    tmp_value = tstate->curexc_value;
+    tmp_tb = tstate->curexc_traceback;
+    tstate->curexc_type = type;
+    tstate->curexc_value = value;
+    tstate->curexc_traceback = tb;
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+#else
+    PyErr_Restore(type, value, tb);
+#endif
+}
+static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
+#if CYTHON_COMPILING_IN_CPYTHON
+    PyThreadState *tstate = PyThreadState_GET();
+    *type = tstate->curexc_type;
+    *value = tstate->curexc_value;
+    *tb = tstate->curexc_traceback;
+    tstate->curexc_type = 0;
+    tstate->curexc_value = 0;
+    tstate->curexc_traceback = 0;
+#else
+    PyErr_Fetch(type, value, tb);
+#endif
+}
+
+#if PY_MAJOR_VERSION < 3
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
+                        CYTHON_UNUSED PyObject *cause) {
+    Py_XINCREF(type);
+    if (!value || value == Py_None)
+        value = NULL;
+    else
+        Py_INCREF(value);
+    if (!tb || tb == Py_None)
+        tb = NULL;
+    else {
+        Py_INCREF(tb);
+        if (!PyTraceBack_Check(tb)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: arg 3 must be a traceback or None");
+            goto raise_error;
+        }
+    }
+    if (PyType_Check(type)) {
+#if CYTHON_COMPILING_IN_PYPY
+        if (!value) {
+            Py_INCREF(Py_None);
+            value = Py_None;
+        }
+#endif
+        PyErr_NormalizeException(&type, &value, &tb);
+    } else {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto raise_error;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(type);
+        Py_INCREF(type);
+        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: exception class must be a subclass of BaseException");
+            goto raise_error;
+        }
+    }
+    __Pyx_ErrRestore(type, value, tb);
+    return;
+raise_error:
+    Py_XDECREF(value);
+    Py_XDECREF(type);
+    Py_XDECREF(tb);
+    return;
+}
+#else
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
+    PyObject* owned_instance = NULL;
+    if (tb == Py_None) {
+        tb = 0;
+    } else if (tb && !PyTraceBack_Check(tb)) {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: arg 3 must be a traceback or None");
+        goto bad;
+    }
+    if (value == Py_None)
+        value = 0;
+    if (PyExceptionInstance_Check(type)) {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto bad;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(value);
+    } else if (PyExceptionClass_Check(type)) {
+        PyObject *instance_class = NULL;
+        if (value && PyExceptionInstance_Check(value)) {
+            instance_class = (PyObject*) Py_TYPE(value);
+            if (instance_class != type) {
+                if (PyObject_IsSubclass(instance_class, type)) {
+                    type = instance_class;
+                } else {
+                    instance_class = NULL;
+                }
+            }
+        }
+        if (!instance_class) {
+            PyObject *args;
+            if (!value)
+                args = PyTuple_New(0);
+            else if (PyTuple_Check(value)) {
+                Py_INCREF(value);
+                args = value;
+            } else
+                args = PyTuple_Pack(1, value);
+            if (!args)
+                goto bad;
+            owned_instance = PyObject_Call(type, args, NULL);
+            Py_DECREF(args);
+            if (!owned_instance)
+                goto bad;
+            value = owned_instance;
+            if (!PyExceptionInstance_Check(value)) {
+                PyErr_Format(PyExc_TypeError,
+                             "calling %R should have returned an instance of "
+                             "BaseException, not %R",
+                             type, Py_TYPE(value));
+                goto bad;
+            }
+        }
+    } else {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: exception class must be a subclass of BaseException");
+        goto bad;
+    }
+#if PY_VERSION_HEX >= 0x03030000
+    if (cause) {
+#else
+    if (cause && cause != Py_None) {
+#endif
+        PyObject *fixed_cause;
+        if (cause == Py_None) {
+            fixed_cause = NULL;
+        } else if (PyExceptionClass_Check(cause)) {
+            fixed_cause = PyObject_CallObject(cause, NULL);
+            if (fixed_cause == NULL)
+                goto bad;
+        } else if (PyExceptionInstance_Check(cause)) {
+            fixed_cause = cause;
+            Py_INCREF(fixed_cause);
+        } else {
+            PyErr_SetString(PyExc_TypeError,
+                            "exception causes must derive from "
+                            "BaseException");
+            goto bad;
+        }
+        PyException_SetCause(value, fixed_cause);
+    }
+    PyErr_SetObject(type, value);
+    if (tb) {
+#if CYTHON_COMPILING_IN_PYPY
+        PyObject *tmp_type, *tmp_value, *tmp_tb;
+        PyErr_Fetch(tmp_type, tmp_value, tmp_tb);
+        Py_INCREF(tb);
+        PyErr_Restore(tmp_type, tmp_value, tb);
+        Py_XDECREF(tmp_tb);
+#else
+        PyThreadState *tstate = PyThreadState_GET();
+        PyObject* tmp_tb = tstate->curexc_traceback;
+        if (tb != tmp_tb) {
+            Py_INCREF(tb);
+            tstate->curexc_traceback = tb;
+            Py_XDECREF(tmp_tb);
+        }
+#endif
+    }
+bad:
+    Py_XDECREF(owned_instance);
+    return;
+}
+#endif
+
+static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
+    int start = 0, mid = 0, end = count - 1;
+    if (end >= 0 && code_line > entries[end].code_line) {
+        return count;
+    }
+    while (start < end) {
+        mid = (start + end) / 2;
+        if (code_line < entries[mid].code_line) {
+            end = mid;
+        } else if (code_line > entries[mid].code_line) {
+             start = mid + 1;
+        } else {
+            return mid;
+        }
+    }
+    if (code_line <= entries[mid].code_line) {
+        return mid;
+    } else {
+        return mid + 1;
+    }
+}
+static PyCodeObject *__pyx_find_code_object(int code_line) {
+    PyCodeObject* code_object;
+    int pos;
+    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
+        return NULL;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
+        return NULL;
+    }
+    code_object = __pyx_code_cache.entries[pos].code_object;
+    Py_INCREF(code_object);
+    return code_object;
+}
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
+    int pos, i;
+    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
+    if (unlikely(!code_line)) {
+        return;
+    }
+    if (unlikely(!entries)) {
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
+        if (likely(entries)) {
+            __pyx_code_cache.entries = entries;
+            __pyx_code_cache.max_count = 64;
+            __pyx_code_cache.count = 1;
+            entries[0].code_line = code_line;
+            entries[0].code_object = code_object;
+            Py_INCREF(code_object);
+        }
+        return;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
+        PyCodeObject* tmp = entries[pos].code_object;
+        entries[pos].code_object = code_object;
+        Py_DECREF(tmp);
+        return;
+    }
+    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
+        int new_max = __pyx_code_cache.max_count + 64;
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
+            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
+        if (unlikely(!entries)) {
+            return;
+        }
+        __pyx_code_cache.entries = entries;
+        __pyx_code_cache.max_count = new_max;
+    }
+    for (i=__pyx_code_cache.count; i>pos; i--) {
+        entries[i] = entries[i-1];
+    }
+    entries[pos].code_line = code_line;
+    entries[pos].code_object = code_object;
+    __pyx_code_cache.count++;
+    Py_INCREF(code_object);
+}
+
+#include "compile.h"
+#include "frameobject.h"
+#include "traceback.h"
+static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
+            const char *funcname, int c_line,
+            int py_line, const char *filename) {
+    PyCodeObject *py_code = 0;
+    PyObject *py_srcfile = 0;
+    PyObject *py_funcname = 0;
+    #if PY_MAJOR_VERSION < 3
+    py_srcfile = PyString_FromString(filename);
+    #else
+    py_srcfile = PyUnicode_FromString(filename);
+    #endif
+    if (!py_srcfile) goto bad;
+    if (c_line) {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        #else
+        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        #endif
+    }
+    else {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromString(funcname);
+        #else
+        py_funcname = PyUnicode_FromString(funcname);
+        #endif
+    }
+    if (!py_funcname) goto bad;
+    py_code = __Pyx_PyCode_New(
+        0,
+        0,
+        0,
+        0,
+        0,
+        __pyx_empty_bytes, /*PyObject *code,*/
+        __pyx_empty_tuple, /*PyObject *consts,*/
+        __pyx_empty_tuple, /*PyObject *names,*/
+        __pyx_empty_tuple, /*PyObject *varnames,*/
+        __pyx_empty_tuple, /*PyObject *freevars,*/
+        __pyx_empty_tuple, /*PyObject *cellvars,*/
+        py_srcfile,   /*PyObject *filename,*/
+        py_funcname,  /*PyObject *name,*/
+        py_line,
+        __pyx_empty_bytes  /*PyObject *lnotab*/
+    );
+    Py_DECREF(py_srcfile);
+    Py_DECREF(py_funcname);
+    return py_code;
+bad:
+    Py_XDECREF(py_srcfile);
+    Py_XDECREF(py_funcname);
+    return NULL;
+}
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename) {
+    PyCodeObject *py_code = 0;
+    PyFrameObject *py_frame = 0;
+    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
+    if (!py_code) {
+        py_code = __Pyx_CreateCodeObjectForTraceback(
+            funcname, c_line, py_line, filename);
+        if (!py_code) goto bad;
+        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
+    }
+    py_frame = PyFrame_New(
+        PyThreadState_GET(), /*PyThreadState *tstate,*/
+        py_code,             /*PyCodeObject *code,*/
+        __pyx_d,      /*PyObject *globals,*/
+        0                    /*PyObject *locals*/
+    );
+    if (!py_frame) goto bad;
+    py_frame->f_lineno = py_line;
+    PyTraceBack_Here(py_frame);
+bad:
+    Py_XDECREF(py_code);
+    Py_XDECREF(py_frame);
+}
+
+#if PY_MAJOR_VERSION < 3
+static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
+    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
+        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags);
+    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
+    return -1;
+}
+static void __Pyx_ReleaseBuffer(Py_buffer *view) {
+    PyObject *obj = view->obj;
+    if (!obj) return;
+    if (PyObject_CheckBuffer(obj)) {
+        PyBuffer_Release(view);
+        return;
+    }
+        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) { __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view); return; }
+    Py_DECREF(obj);
+    view->obj = NULL;
+}
+#endif
+
+
+          static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
+    PyObject *empty_list = 0;
+    PyObject *module = 0;
+    PyObject *global_dict = 0;
+    PyObject *empty_dict = 0;
+    PyObject *list;
+    #if PY_VERSION_HEX < 0x03030000
+    PyObject *py_import;
+    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
+    if (!py_import)
+        goto bad;
+    #endif
+    if (from_list)
+        list = from_list;
+    else {
+        empty_list = PyList_New(0);
+        if (!empty_list)
+            goto bad;
+        list = empty_list;
+    }
+    global_dict = PyModule_GetDict(__pyx_m);
+    if (!global_dict)
+        goto bad;
+    empty_dict = PyDict_New();
+    if (!empty_dict)
+        goto bad;
+    {
+        #if PY_MAJOR_VERSION >= 3
+        if (level == -1) {
+            if (strchr(__Pyx_MODULE_NAME, '.')) {
+                #if PY_VERSION_HEX < 0x03030000
+                PyObject *py_level = PyInt_FromLong(1);
+                if (!py_level)
+                    goto bad;
+                module = PyObject_CallFunctionObjArgs(py_import,
+                    name, global_dict, empty_dict, list, py_level, NULL);
+                Py_DECREF(py_level);
+                #else
+                module = PyImport_ImportModuleLevelObject(
+                    name, global_dict, empty_dict, list, 1);
+                #endif
+                if (!module) {
+                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
+                        goto bad;
+                    PyErr_Clear();
+                }
+            }
+            level = 0;
+        }
+        #endif
+        if (!module) {
+            #if PY_VERSION_HEX < 0x03030000
+            PyObject *py_level = PyInt_FromLong(level);
+            if (!py_level)
+                goto bad;
+            module = PyObject_CallFunctionObjArgs(py_import,
+                name, global_dict, empty_dict, list, py_level, NULL);
+            Py_DECREF(py_level);
+            #else
+            module = PyImport_ImportModuleLevelObject(
+                name, global_dict, empty_dict, list, level);
+            #endif
+        }
+    }
+bad:
+    #if PY_VERSION_HEX < 0x03030000
+    Py_XDECREF(py_import);
+    #endif
+    Py_XDECREF(empty_list);
+    Py_XDECREF(empty_dict);
+    return module;
+}
+
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
+    const int neg_one = (int) -1, const_zero = 0;
+    const int is_unsigned = neg_one > const_zero;
+    if (is_unsigned) {
+        if (sizeof(int) < sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(int) <= sizeof(unsigned long)) {
+            return PyLong_FromUnsignedLong((unsigned long) value);
+        } else if (sizeof(int) <= sizeof(unsigned long long)) {
+            return PyLong_FromUnsignedLongLong((unsigned long long) value);
+        }
+    } else {
+        if (sizeof(int) <= sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(int) <= sizeof(long long)) {
+            return PyLong_FromLongLong((long long) value);
+        }
+    }
+    {
+        int one = 1; int little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&value;
+        return _PyLong_FromByteArray(bytes, sizeof(int),
+                                     little, !is_unsigned);
+    }
+}
+
+#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)       \
+    {                                                                     \
+        func_type value = func_value;                                     \
+        if (sizeof(target_type) < sizeof(func_type)) {                    \
+            if (unlikely(value != (func_type) (target_type) value)) {     \
+                func_type zero = 0;                                       \
+                if (is_unsigned && unlikely(value < zero))                \
+                    goto raise_neg_overflow;                              \
+                else                                                      \
+                    goto raise_overflow;                                  \
+            }                                                             \
+        }                                                                 \
+        return (target_type) value;                                       \
+    }
+
+#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
+ #if CYTHON_USE_PYLONG_INTERNALS
+  #include "longintrepr.h"
+ #endif
+#endif
+
+static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
+    const int neg_one = (int) -1, const_zero = 0;
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if (sizeof(int) < sizeof(long)) {
+            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (int) val;
+        }
+    } else
+#endif
+    if (likely(PyLong_Check(x))) {
+        if (is_unsigned) {
+#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
+ #if CYTHON_USE_PYLONG_INTERNALS
+            switch (Py_SIZE(x)) {
+                case  0: return 0;
+                case  1: __PYX_VERIFY_RETURN_INT(int, digit, ((PyLongObject*)x)->ob_digit[0]);
+            }
+ #endif
+#endif
+            if (unlikely(Py_SIZE(x) < 0)) {
+                goto raise_neg_overflow;
+            }
+            if (sizeof(int) <= sizeof(unsigned long)) {
+                __PYX_VERIFY_RETURN_INT(int, unsigned long, PyLong_AsUnsignedLong(x))
+            } else if (sizeof(int) <= sizeof(unsigned long long)) {
+                __PYX_VERIFY_RETURN_INT(int, unsigned long long, PyLong_AsUnsignedLongLong(x))
+            }
+        } else {
+#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
+ #if CYTHON_USE_PYLONG_INTERNALS
+            switch (Py_SIZE(x)) {
+                case  0: return 0;
+                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +(((PyLongObject*)x)->ob_digit[0]));
+                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
+            }
+ #endif
+#endif
+            if (sizeof(int) <= sizeof(long)) {
+                __PYX_VERIFY_RETURN_INT(int, long, PyLong_AsLong(x))
+            } else if (sizeof(int) <= sizeof(long long)) {
+                __PYX_VERIFY_RETURN_INT(int, long long, PyLong_AsLongLong(x))
+            }
+        }
+        {
+#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
+            PyErr_SetString(PyExc_RuntimeError,
+                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
+#else
+            int val;
+            PyObject *v = __Pyx_PyNumber_Int(x);
+ #if PY_MAJOR_VERSION < 3
+            if (likely(v) && !PyLong_Check(v)) {
+                PyObject *tmp = v;
+                v = PyNumber_Long(tmp);
+                Py_DECREF(tmp);
+            }
+ #endif
+            if (likely(v)) {
+                int one = 1; int is_little = (int)*(unsigned char *)&one;
+                unsigned char *bytes = (unsigned char *)&val;
+                int ret = _PyLong_AsByteArray((PyLongObject *)v,
+                                              bytes, sizeof(val),
+                                              is_little, !is_unsigned);
+                Py_DECREF(v);
+                if (likely(!ret))
+                    return val;
+            }
+#endif
+            return (int) -1;
+        }
+    } else {
+        int val;
+        PyObject *tmp = __Pyx_PyNumber_Int(x);
+        if (!tmp) return (int) -1;
+        val = __Pyx_PyInt_As_int(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to int");
+    return (int) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to int");
+    return (int) -1;
+}
+
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return ::std::complex< float >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return x + y*(__pyx_t_float_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      __pyx_t_float_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+#if CYTHON_CCOMPLEX
+#else
+    static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        float denom = b.real * b.real + b.imag * b.imag;
+        z.real = (a.real * b.real + a.imag * b.imag) / denom;
+        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrtf(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypotf(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_powf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+            __pyx_t_float_complex z;
+            float r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    float denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        z = __Pyx_c_prodf(a, a);
+                        return __Pyx_c_prodf(a, a);
+                    case 3:
+                        z = __Pyx_c_prodf(a, a);
+                        return __Pyx_c_prodf(z, a);
+                    case 4:
+                        z = __Pyx_c_prodf(a, a);
+                        return __Pyx_c_prodf(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                }
+                r = a.real;
+                theta = 0;
+            } else {
+                r = __Pyx_c_absf(a);
+                theta = atan2f(a.imag, a.real);
+            }
+            lnr = logf(r);
+            z_r = expf(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cosf(z_theta);
+            z.imag = z_r * sinf(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return ::std::complex< double >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return x + y*(__pyx_t_double_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      __pyx_t_double_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+#if CYTHON_CCOMPLEX
+#else
+    static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        double denom = b.real * b.real + b.imag * b.imag;
+        z.real = (a.real * b.real + a.imag * b.imag) / denom;
+        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrt(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypot(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+            __pyx_t_double_complex z;
+            double r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    double denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        z = __Pyx_c_prod(a, a);
+                        return __Pyx_c_prod(a, a);
+                    case 3:
+                        z = __Pyx_c_prod(a, a);
+                        return __Pyx_c_prod(z, a);
+                    case 4:
+                        z = __Pyx_c_prod(a, a);
+                        return __Pyx_c_prod(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                }
+                r = a.real;
+                theta = 0;
+            } else {
+                r = __Pyx_c_abs(a);
+                theta = atan2(a.imag, a.real);
+            }
+            lnr = log(r);
+            z_r = exp(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cos(z_theta);
+            z.imag = z_r * sin(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
+    const long neg_one = (long) -1, const_zero = 0;
+    const int is_unsigned = neg_one > const_zero;
+    if (is_unsigned) {
+        if (sizeof(long) < sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(long) <= sizeof(unsigned long)) {
+            return PyLong_FromUnsignedLong((unsigned long) value);
+        } else if (sizeof(long) <= sizeof(unsigned long long)) {
+            return PyLong_FromUnsignedLongLong((unsigned long long) value);
+        }
+    } else {
+        if (sizeof(long) <= sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(long) <= sizeof(long long)) {
+            return PyLong_FromLongLong((long long) value);
+        }
+    }
+    {
+        int one = 1; int little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&value;
+        return _PyLong_FromByteArray(bytes, sizeof(long),
+                                     little, !is_unsigned);
+    }
+}
+
+static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
+    const long neg_one = (long) -1, const_zero = 0;
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if (sizeof(long) < sizeof(long)) {
+            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (long) val;
+        }
+    } else
+#endif
+    if (likely(PyLong_Check(x))) {
+        if (is_unsigned) {
+#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
+ #if CYTHON_USE_PYLONG_INTERNALS
+            switch (Py_SIZE(x)) {
+                case  0: return 0;
+                case  1: __PYX_VERIFY_RETURN_INT(long, digit, ((PyLongObject*)x)->ob_digit[0]);
+            }
+ #endif
+#endif
+            if (unlikely(Py_SIZE(x) < 0)) {
+                goto raise_neg_overflow;
+            }
+            if (sizeof(long) <= sizeof(unsigned long)) {
+                __PYX_VERIFY_RETURN_INT(long, unsigned long, PyLong_AsUnsignedLong(x))
+            } else if (sizeof(long) <= sizeof(unsigned long long)) {
+                __PYX_VERIFY_RETURN_INT(long, unsigned long long, PyLong_AsUnsignedLongLong(x))
+            }
+        } else {
+#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
+ #if CYTHON_USE_PYLONG_INTERNALS
+            switch (Py_SIZE(x)) {
+                case  0: return 0;
+                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +(((PyLongObject*)x)->ob_digit[0]));
+                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
+            }
+ #endif
+#endif
+            if (sizeof(long) <= sizeof(long)) {
+                __PYX_VERIFY_RETURN_INT(long, long, PyLong_AsLong(x))
+            } else if (sizeof(long) <= sizeof(long long)) {
+                __PYX_VERIFY_RETURN_INT(long, long long, PyLong_AsLongLong(x))
+            }
+        }
+        {
+#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
+            PyErr_SetString(PyExc_RuntimeError,
+                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
+#else
+            long val;
+            PyObject *v = __Pyx_PyNumber_Int(x);
+ #if PY_MAJOR_VERSION < 3
+            if (likely(v) && !PyLong_Check(v)) {
+                PyObject *tmp = v;
+                v = PyNumber_Long(tmp);
+                Py_DECREF(tmp);
+            }
+ #endif
+            if (likely(v)) {
+                int one = 1; int is_little = (int)*(unsigned char *)&one;
+                unsigned char *bytes = (unsigned char *)&val;
+                int ret = _PyLong_AsByteArray((PyLongObject *)v,
+                                              bytes, sizeof(val),
+                                              is_little, !is_unsigned);
+                Py_DECREF(v);
+                if (likely(!ret))
+                    return val;
+            }
+#endif
+            return (long) -1;
+        }
+    } else {
+        long val;
+        PyObject *tmp = __Pyx_PyNumber_Int(x);
+        if (!tmp) return (long) -1;
+        val = __Pyx_PyInt_As_long(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to long");
+    return (long) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to long");
+    return (long) -1;
+}
+
+static int __Pyx_check_binary_version(void) {
+    char ctversion[4], rtversion[4];
+    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
+    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
+    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
+        char message[200];
+        PyOS_snprintf(message, sizeof(message),
+                      "compiletime version %s of module '%.100s' "
+                      "does not match runtime version %s",
+                      ctversion, __Pyx_MODULE_NAME, rtversion);
+        return PyErr_WarnEx(NULL, message, 1);
+    }
+    return 0;
+}
+
+#ifndef __PYX_HAVE_RT_ImportModule
+#define __PYX_HAVE_RT_ImportModule
+static PyObject *__Pyx_ImportModule(const char *name) {
+    PyObject *py_name = 0;
+    PyObject *py_module = 0;
+    py_name = __Pyx_PyIdentifier_FromString(name);
+    if (!py_name)
+        goto bad;
+    py_module = PyImport_Import(py_name);
+    Py_DECREF(py_name);
+    return py_module;
+bad:
+    Py_XDECREF(py_name);
+    return 0;
+}
+#endif
+
+#ifndef __PYX_HAVE_RT_ImportType
+#define __PYX_HAVE_RT_ImportType
+static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
+    size_t size, int strict)
+{
+    PyObject *py_module = 0;
+    PyObject *result = 0;
+    PyObject *py_name = 0;
+    char warning[200];
+    Py_ssize_t basicsize;
+#ifdef Py_LIMITED_API
+    PyObject *py_basicsize;
+#endif
+    py_module = __Pyx_ImportModule(module_name);
+    if (!py_module)
+        goto bad;
+    py_name = __Pyx_PyIdentifier_FromString(class_name);
+    if (!py_name)
+        goto bad;
+    result = PyObject_GetAttr(py_module, py_name);
+    Py_DECREF(py_name);
+    py_name = 0;
+    Py_DECREF(py_module);
+    py_module = 0;
+    if (!result)
+        goto bad;
+    if (!PyType_Check(result)) {
+        PyErr_Format(PyExc_TypeError,
+            "%.200s.%.200s is not a type object",
+            module_name, class_name);
+        goto bad;
+    }
+#ifndef Py_LIMITED_API
+    basicsize = ((PyTypeObject *)result)->tp_basicsize;
+#else
+    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
+    if (!py_basicsize)
+        goto bad;
+    basicsize = PyLong_AsSsize_t(py_basicsize);
+    Py_DECREF(py_basicsize);
+    py_basicsize = 0;
+    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
+        goto bad;
+#endif
+    if (!strict && (size_t)basicsize > size) {
+        PyOS_snprintf(warning, sizeof(warning),
+            "%s.%s size changed, may indicate binary incompatibility",
+            module_name, class_name);
+        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
+    }
+    else if ((size_t)basicsize != size) {
+        PyErr_Format(PyExc_ValueError,
+            "%.200s.%.200s has the wrong size, try recompiling",
+            module_name, class_name);
+        goto bad;
+    }
+    return (PyTypeObject *)result;
+bad:
+    Py_XDECREF(py_module);
+    Py_XDECREF(result);
+    return NULL;
+}
+#endif
+
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
+    while (t->p) {
+        #if PY_MAJOR_VERSION < 3
+        if (t->is_unicode) {
+            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
+        } else if (t->intern) {
+            *t->p = PyString_InternFromString(t->s);
+        } else {
+            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
+        }
+        #else
+        if (t->is_unicode | t->is_str) {
+            if (t->intern) {
+                *t->p = PyUnicode_InternFromString(t->s);
+            } else if (t->encoding) {
+                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
+            } else {
+                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
+            }
+        } else {
+            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
+        }
+        #endif
+        if (!*t->p)
+            return -1;
+        ++t;
+    }
+    return 0;
+}
+
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
+    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
+}
+static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
+    Py_ssize_t ignore;
+    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
+}
+static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+    if (
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+            __Pyx_sys_getdefaultencoding_not_ascii &&
+#endif
+            PyUnicode_Check(o)) {
+#if PY_VERSION_HEX < 0x03030000
+        char* defenc_c;
+        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
+        if (!defenc) return NULL;
+        defenc_c = PyBytes_AS_STRING(defenc);
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+        {
+            char* end = defenc_c + PyBytes_GET_SIZE(defenc);
+            char* c;
+            for (c = defenc_c; c < end; c++) {
+                if ((unsigned char) (*c) >= 128) {
+                    PyUnicode_AsASCIIString(o);
+                    return NULL;
+                }
+            }
+        }
+#endif
+        *length = PyBytes_GET_SIZE(defenc);
+        return defenc_c;
+#else
+        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+        if (PyUnicode_IS_ASCII(o)) {
+            *length = PyUnicode_GET_LENGTH(o);
+            return PyUnicode_AsUTF8(o);
+        } else {
+            PyUnicode_AsASCIIString(o);
+            return NULL;
+        }
+#else
+        return PyUnicode_AsUTF8AndSize(o, length);
+#endif
+#endif
+    } else
+#endif
+#if !CYTHON_COMPILING_IN_PYPY
+    if (PyByteArray_Check(o)) {
+        *length = PyByteArray_GET_SIZE(o);
+        return PyByteArray_AS_STRING(o);
+    } else
+#endif
+    {
+        char* result;
+        int r = PyBytes_AsStringAndSize(o, &result, length);
+        if (unlikely(r < 0)) {
+            return NULL;
+        } else {
+            return result;
+        }
+    }
+}
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
+   int is_true = x == Py_True;
+   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
+   else return PyObject_IsTrue(x);
+}
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
+  PyNumberMethods *m;
+  const char *name = NULL;
+  PyObject *res = NULL;
+#if PY_MAJOR_VERSION < 3
+  if (PyInt_Check(x) || PyLong_Check(x))
+#else
+  if (PyLong_Check(x))
+#endif
+    return Py_INCREF(x), x;
+  m = Py_TYPE(x)->tp_as_number;
+#if PY_MAJOR_VERSION < 3
+  if (m && m->nb_int) {
+    name = "int";
+    res = PyNumber_Int(x);
+  }
+  else if (m && m->nb_long) {
+    name = "long";
+    res = PyNumber_Long(x);
+  }
+#else
+  if (m && m->nb_int) {
+    name = "int";
+    res = PyNumber_Long(x);
+  }
+#endif
+  if (res) {
+#if PY_MAJOR_VERSION < 3
+    if (!PyInt_Check(res) && !PyLong_Check(res)) {
+#else
+    if (!PyLong_Check(res)) {
+#endif
+      PyErr_Format(PyExc_TypeError,
+                   "__%.4s__ returned non-%.4s (type %.200s)",
+                   name, name, Py_TYPE(res)->tp_name);
+      Py_DECREF(res);
+      return NULL;
+    }
+  }
+  else if (!PyErr_Occurred()) {
+    PyErr_SetString(PyExc_TypeError,
+                    "an integer is required");
+  }
+  return res;
+}
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
+  Py_ssize_t ival;
+  PyObject *x;
+#if PY_MAJOR_VERSION < 3
+  if (likely(PyInt_CheckExact(b)))
+      return PyInt_AS_LONG(b);
+#endif
+  if (likely(PyLong_CheckExact(b))) {
+    #if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
+     #if CYTHON_USE_PYLONG_INTERNALS
+       switch (Py_SIZE(b)) {
+       case -1: return -(sdigit)((PyLongObject*)b)->ob_digit[0];
+       case  0: return 0;
+       case  1: return ((PyLongObject*)b)->ob_digit[0];
+       }
+     #endif
+    #endif
+    return PyLong_AsSsize_t(b);
+  }
+  x = PyNumber_Index(b);
+  if (!x) return -1;
+  ival = PyInt_AsSsize_t(x);
+  Py_DECREF(x);
+  return ival;
+}
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
+    return PyInt_FromSize_t(ival);
+}
+
+
+#endif /* Py_PYTHON_H */